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A Chinese time ontology for the Semantic Web
Knowledge-Based Systems 24 (2011) 1057–1074
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Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys
A Chinese time ontology for the Semantic Web Chunxia Zhang a,⇑, Cungen Cao b, Yuefei Sui b, Xindong Wu c,d a
School of Software, Beijing Institute of Technology, Beijing 100081, China Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China c Department of Computer Science, University of Vermont, Burlington, VT 05405, USA d School of Computer Science and Information Technology, Hefei University of Technology, Hefei 230009, China b
a r t i c l e
i n f o
Article history: Received 23 December 2009 Received in revised form 29 April 2011 Accepted 29 April 2011 Available online 6 May 2011 Keywords: Time ontology Semantic Web Chinese time ontology Temporal entities Temporal representation
a b s t r a c t Representation of and reasoning with temporal knowledge are fundamental in information systems that involve changes and actions. To build such systems, a time ontology is demanded. The development of a time ontology is also an indispensable part of effort to realize the Semantic Web. Nevertheless, our practice shows that any practical time ontology is closely related with a specific calendar, culture or history. To this end, this paper presents a Chinese time ontology for knowledge systems and web services which involve temporal entities or temporal properties. First, we define a base time ontology. As a core component, it consists of a time system, a timing system, a Gregorian timing system, and a timing ontology. Upon this base ontology, other parts of the Chinese time ontology are finally constructed, including the traditional Chinese timing system, temporal representation in Chinese idiosyncratic ways, and transformation between temporal entities in the Gregorian timing system and temporal entities in the traditional Chinese timing system. We will argue that the base time ontology is not only a basic and integral part of the Chinese time ontology, but also a base for constructing other time ontologies. 2011 Elsevier B.V. All rights reserved.
1. Introduction One of the crucial problems in information and knowledge systems that involve action and change is the representation of and reasoning with time. To develop such systems, a time ontology is demanded. Building a time ontology is also necessary to realize the Semantic Web, which aims to provide automated web services based on the descriptions of the contents and capabilities of web resources [27,24]. A time ontology is a specification of a conceptualization for temporal knowledge. Currently, much effort has been made on building explicit time ontologies, such as the DAML ontology of time [17,18,42], the time ontology in OWL [47], KSL time ontology [44], the time ontology in KIF [48], Times and Dates in Cyc knowledge base [50], the time of DAML-S [43], the temporal portion of IEEE Standard Upper Ontology [49], and other works [11,15,28,32]. In working on time ontologies, our experience indicates that time ontologies are closely related with specific nations or cultures, though they may share a common part. This is especially true if nations, e.g. the Chinese nation, have a long history. For example, in our work on knowledge processing of Chinese historical knowledge [4], timing methods are associated with various historical events; in fact, each Chinese dynasty or kingdom had its ⇑ Corresponding author. E-mail addresses: [email protected] (C. Zhang), [email protected] (C. Cao), [email protected] (Y. Sui), [email protected] (X. Wu). 0950-7051/$ - see front matter 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.knosys.2011.04.021
own particular timing method. As another example, in our work on agricultural knowledge acquisition [5], we found that ancient farmers used a timing method of 24 Solar Terms for farming (e.g. what crops and animals are planted and raised during what solar terms?). Although no one exactly knows when this approach was created, it is still one of the dominant timing methods in Chinese societies. In spite of the great progresses in the past years, there are still two important issues about time ontologies that need to be further addressed, which constitute the motivation of this paper. One is that most existing ontologies count and express time according to the Gregorian calendar, and those ontologies are incapable of computing and representing time for people in societies with their own calendars. In other words, the effect of calendars in constructing time ontologies is simply ignored. However, calendars play an important role in building time ontologies. Actually, calendars are the basis of computing durations of and relationships between time units, and different calendars constitute different timing systems. In addition, to realize the Semantic Web, it is necessary for machines to be able to process and understand the semantics of temporal entities in various calendars on the World Wide Web [26]. Hence, it is indispensable to build up mappings between temporal entities in different timing systems within the same or different calendars. Another issue is the diversity of temporal computing and representation. Current time ontologies compute and express time mainly in a manner of the calendar date. However, there are other
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various approaches of computing and representing time that are related to a country’s culture, history, and agriculture and so on. People in different social-cultural contexts use different approaches to count and express time. This knowledge should also be addressed when building time ontologies. In this paper, we present a Chinese time ontology based on the current Chinese calendars: the Gregorian calendar and the traditional Chinese calendar. The Gregorian calendar is a kind of solar calendar, and is used almost everywhere in the world. The traditional Chinese calendar is a type of lunisolar calendar [39,51]. The ontology is developed for web services and knowledge systems that involve temporal entities or temporal properties. We build our ontology in two steps. First, we build a core component, called the base time ontology. Specifically, it consists of a time system, a timing system, a Gregorian timing system, and a timing ontology. Here, the Gregorian timing system is employed as a timing system based on the Gregorian calendar. Second, upon this base time ontology, we develop the other parts of the Chinese time ontology, including a traditional Chinese timing system, temporal representation in Chinese idiosyncratic ways, and transformation (mapping) between temporal entities in the Gregorian timing system and temporal entities in the traditional Chinese timing system. Here, the traditional Chinese timing system is a timing system founded on the traditional Chinese calendar. Furthermore, we will also argue that the base time ontology is not only a basic and integral part of the Chinese time ontology, but also a base for constructing other time ontologies. The remainder of this paper is organized as follows. Section 2 reviews the related work of time ontologies. Section 3 presents our Chinese time ontology. Section 4 compares our Chinese time ontology with other time ontologies, and introduces its applications in question answering and web services. The discussion is given in Section 5. Section 6 concludes this paper.
2. Related work Time is a basic attribute of data, information, and knowledge [7]. Temporal information processing has become a significant technique in the fields of information system, the Semantic Web, and natural language processing [25,33]. Time ontologies provide the measurement, computation and representation of time. Therefore, they are especially important for a variety of information systems such as electronic commerce, data warehouse, data mining, and decision support systems [10,13,20,21,33]. Temporal information has also penetrated into every aspect of the Internet; hence the specification of temporal information is necessary to realize the Semantic Web. Time ontologies are intended to give a specification of a conceptualization of temporal contents of web information and temporal properties of web services [25]. Natural language text is a main carrier of the web information. Time ontologies also play an important role in many natural language processing applications such as information retrieval, question answering, and text summarization [25,30]. It is difficult for applications involved in temporal knowledge to make significant progress without the explicit representation of the semantics of temporal information or properties. It is necessary to build a Chinese time ontology for processing temporal information which are represented in Chinese ways using any formal language or natural language. The DAML ontology of time [17,18,42] and the time ontology in OWL [47] use the first-order predicate calculus to represent temporal concepts and properties, including topological relations among instants, intervals, and events, measures of duration, the Gregorian calendar and clock terms, and times and durations. These two ontologies regard instants and intervals as temporal primitives. Times and Dates in Cyc knowledge base [50] aims to
build a temporal knowledge base of human commonsense knowledge. This knowledge base consists of assertions, rules, and commonsense ideas, which describe time points, properties of and relations between temporal objects, the calendar, and time of day and so on. The representation language of this knowledge base is the language CycL based on predicate calculus [50]. KSL time ontology treats time points and time intervals as temporal primitives on a time line [44]. This ontology is composed of the temporal class hierarchy structure, relations between time points and time intervals, time granularity and so on. The weaknesses of present time ontologies are given as follows. (1) The current ontologies are built based on the Gregorian calendar, so they can not compute and represent time expressed based on other calendars. Further, they neither consider the impacts of different calendars on time ontologies, nor build a conceptual model for various calendars. (2) They treat topological temporal relations, durations measure, times and durations description, and the calendar and clock, at a same conceptual level. In fact, the latter three parts are dependent on the Gregorian calendar. In our time ontology, those three parts are ingredients of the Gregorian timing system. (3) They neither give explicit classification criterions for temporal concepts, nor formal axioms for temporal concepts and their attributes. (4) Present ontologies compute and represent time in the form of the calendar date. However, they do not investigate the effect of a culture, history, and agriculture on temporal representations. The research tendency about time ontologies is the representation and transformation of deictic time (such as ‘‘last year”), aggregates of temporal entities (such as ‘‘every Monday”), and vague temporal entities (such as ‘‘recently”). A number of time theories have been proposed as formal bases for temporal knowledge representation and reasoning. Bruce [3], Kahn and Gorry [19], McCarthy and Hayes [22], McDermott [23], Shoham [31], and Halpern [16] all used the instant-based theory in their respective artificial intelligent systems. This theory was criticized for being unnatural or counterintuitive, and it also encountered the so-called Dividing Instant Problem [35]. Allen regarded the period as the ontological primitive of time [2], while Galton [12], Vila [34] treated both instants and intervals as time primitives. We choose instants and intervals as temporal primitives. Because the instant- and period-based time theory is more natural and intuitive, and can describe temporal knowledge more conveniently than a pure instant- or period-based time theory. It also satisfactorily addresses the problems that are confronted by the other two time theories, such as the Dividing Instant Problem and the expression of instantaneous events and instantaneous holding of the fluent [1,35]. Ontology can be classified into generic ontology, domain ontology, application ontology, and representation ontology. The research scope of this paper is to build a time ontology which is a kind of domain ontology. This paper focuses on two research questions: (1) how to build a base time ontology, which can be employed as a common core component of different time ontologies, and is irrelevant to any calendar, culture or language. (2) How to build a time ontology based on the traditional Chinese calendar and the Gregorian calendar. In this process, we have two assumptions about time primitives and time structure. One is that there are two time primitives: time instant and time interval, the other is that the time structure is linear and continuous. In contrast to the existing works, the main innovations of this paper are depicted as follows. (1) We propose the time system, the timing system, the timing ontology, and the Gregorian timing system to constitute the base time ontology. The former three components are independent of any calendar, language, or culture, while the last component acts as ‘‘a time intermediator”. (2) In order to process temporal information represented based on different calendars, this paper provides an approach for building the
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time ontologies based on different calendars. (3) Our time ontology builds a formal and explicit conceptualization of the temporal representation and transformation relating to the Gregorian calendar and the traditional Chinese calendar. In addition, we use a divide and conquer technique to represent temporal entity and transform temporal entities in different timing systems. Our time ontology provides various representation methods for different kinds of temporal entities in the traditional Chinese timing system, and constitutive methods of combined representations of these entities. Furthermore, temporal entities in the traditional Chinese timing system can be transformed into the corresponding temporal entities in the Gregorian timing system by using the converting formulas in this paper, and vise versa. The benefits and significances of this paper are given from the aspects of the base time ontology, the time ontology building method, and the temporal representation and transformation. (1) The time system, the timing system, and the timing ontology in the base time ontology are built in aspects of topology model, measure and representation model, and semantic model of time. Moreover, they are not affected by any calendar, culture, and representation language. From another point of view, conceptual models of time can be divided into a model involving measurement and a model not involving measurement. In this paper, the timing system and the timing ontology constitute the former model, while the time system is the latter model. The timing system is a conceptual model for various calendars, and the timing ontology is a conceptual model for temporal entities represented based on different calendars. Therefore, our base time ontology can be used into different levels of temporal representation and information applications across different calendars, cultures, and representation languages. (2) Our approach of building the Chinese time ontology complies with the criteria of ontology development: clarity, extendibility, and minimal ontological commitment [14]. (a) Clarity means that definitions of terms should be objective, complete, and be stated in logical axioms, where a complete definition of a term means that it is defined by necessary and sufficient conditions [14]. For example, each class of temporal entities in the timing ontology is specified with formal and complete definitional axioms. (b) An ontology with the minimal ontology commitment should specify the minimal constraints about the objects being modeled [14]. As an illustration, in the Gregorian timing system and the traditional Chinese timing system, starting times, ending times, and temporal lengths of the three basic time units (including year, month, and day) are given in formal axioms, and starting times, ending times, and temporal lengths of other time units can be defined based on those axioms. (c) An ontology with extendibility should provide a conceptual basis, and new terms can be defined based on present terms without the revision of the present ontology [14]. For instance, for the temporal representation in the traditional Chinese timing system, any new representation method and its transformation method of lunar year, lunar month, lunar day, and hour can be easily added to the present ontology; and any new combined representation of temporal entities can also be added. Hence, our ontology building method makes our ontology and can make other time ontologies built by that method with more flexibility, portability, and extendibility. (3) For the temporal representation and transformation, a divide and conquer technique is employed to express temporal entity and transform temporal entities in different tim-
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ing systems. For a temporal entity te in the traditional Chinese timing system, it can be divided into one or multiple temporal entities te11, te12, . . . , te1k, each of which involve only a time unit, according to representing methods of lunar years, lunar months, lunar days, and hours. Here, te1i (i = 1, 2, . . . , k) includes one or multiple representing methods of a time unit. Thereby, we build constitutive methods of combined representation of different kinds of temporal entities. In addition, te11, te12, . . . , te1k can be transformed into temporal entity te21, te22, . . . , te2k in the Gregorian timing system according to the transforming formulas in this paper, respectively. Further, te21, te22, . . . , te2k are integrated to constitute a temporal entity in the Gregorian timing system, which is the corresponding temporal entity of te. Thus, this kind of technique makes it easier to express various granularities of temporal entities in the traditional Chinese timing system and to transform between them and temporal entities in the Gregorian timing system. 3. A Chinese time ontology We will present the framework of our Chinese time ontology, the contents of the base time ontology and other parts of the Chinese time ontology in this section. 3.1. The framework of the Chinese time ontology The framework of the Chinese time ontology is illustrated in Fig. 1. The base time ontology is composed of a time system, a timing system, and a timing ontology, which are built on topological level, measure and representation level, and semantic level of time, respectively. The time system gives the time primitives, the time structure, and the topological relations between instants, intervals, and events. The timing system is a formal and general conceptual model for various methods of computing and representing time. For temporal entities expressed by any kind of timing system in any formal or natural language, the timing ontology includes classes of temporal entities, attributes of classes, relationships between classes, and semantic axioms constraining the interpretation and application of these terms. Therefore, the time system, the timing system, and the timing ontology are independent of any calendar, culture, and language. The Gregorian timing system and the traditional Chinese timing system are two instances of the timing system. The Gregorian timing system consists of axioms about instants and intervals in the Gregorian calendar, and the representation of temporal entities based on this calendar. This system is included in the base time ontology. The traditional Chinese timing system contains axioms about instants and intervals in the traditional Chinese calendar and the representation of temporal entities founded on this calendar. Other parts of our Chinese time ontology comprise the traditional Chinese timing system and the transformation between temporal entities in the Gregorian timing system and those in the traditional Chinese timing system. In the following, we use the first-order predicate calculus as the representation language of our time ontology, which has been employed to represent various domain-specific ontologies including mathematics, archaeology, geography, and history and so on in our former works [5,36]. It is noted that the time ontology has nothing to do with any ontology representation language. 3.2. The base time ontology We assume a linear and continuous time structure for the Chinese time ontology. That is, the time line is isomorphic to the set of real numbers and is unbounded.
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Part 1:The Base Time Ontology
Our Chinese Time Ontology
The Time System Topological Level The Timing System Measure and Representation Level
The Gregorian Timing System
Axioms about the Gregorian Calendar Intervals and Instants Representation of Temporal Entities based on the Gregorian Calendar
The timing Ontology Semantic Level Transformation between Temporal Entities
IS-A Relation Part-Whole Relation Transformation Relation
The Traditional Chinese Timing System
Axioms about the Traditional Chinese Calendar Intervals and Instants Representation of Temporal Entities based on the Traditional Chinese Calendar
Part 2: Other Parts of Our Chinese Time Ontology Fig. 1. The framework of our Chinese time ontology.
3.2.1. The time system As argued previously, we consider the time system to have two time primitives: time instant (or instant for short) and time interval (or interval for short). The time system is intended to give topological temporal relations between instants themselves, between intervals themselves, and between instants and intervals, and relations between events and time [37]. Let the type of the time instants be r and the type of the time intervals be s. A time system contains (1) Three predicates instant(t), interval(T) and temporal-entity(x) to denote that t is an instant, T is an interval and x is a temporal entity, respectively. (2) Two functions startFn(x) and endFn(x): s ? r. (3) Two predicates before(t1, t2): r r ? X, inside(t, T): r s ? X, where X is the type of Boolean values {true, false}. By the types of functions and predicates, we have the following formal axioms. (1) Instants and intervals are disjoint; that is, a temporal entity is either an instant or an interval, as shown in axiom (c) below. (a) "t (instant(t) ? temporal-entity(t)) (b) "T (interval(T) ? temporal-entity(T)) (c) "x (temporal-entity(x) ? (instant(x) ^ : interval(x)) _ (:instant (x) ^ interval(x))) (2) before(t1, t2) means that t1 is before t2, which gives directionality to time. The before relation is irreflexive, asymmetric, transitive and linear, as shown in the following axioms (a)–(d): (a) "t1 (:before(t1, t1)) (b) "t1 "t2 (before(t1, t2) ? :before(t2, t1)) (c) "t1 "t2 "t3 (before(t1, t2) ^ before(t2, t3) ? before(t1, t3)) (d) "t1 "t2 (before(t1, t2)_before(t2, t1)_(t1 = t2)) (3) startFn(T) and endFn (T) represent the starting and ending instants of T, respectively. Axioms (c) and (d) below say that there exist unique starting and ending instants for each interval. The starting instant of T is always before its ending one, shown in axiom (e). (a) "T "t ((startFn(T) = t) ? interval(T) ^ instant(t)) (b) "T "t ((endFn (T) = t) ? interval(T) ^ instant(t))
(c) "T "t1 "t2 ((startFn(T) = t1) ^ (startFn(T) = t2) ? t1 = t2) (d) "T "t1 "t2 ((endFn (T) = t1) ^ (endFn (T) = t2) ? t1 = t2) (e) "T "t1"t2 ((startFn(T) = t1) ^ (endFn (T) = t2) ? before(t1, t2)) (4) The predicate inside(t, T) expresses a relation between an instant and an interval, meaning that t is an instant within T. The following axiom means that every interval is closed in the sense that it contains its starting and ending instants.
8t 8tTðinsideðt; TÞ $ ðt ¼ startFnðTÞÞ _ ðt ¼ endFnðTÞÞ _ ðbeforeðstartFnðTÞ; tÞ ^ beforeðt; endFnðTÞÞÞÞ (5) Relations between intervals are given by the following axioms, which are based on the before relations between their beginning and ending instants. (a) precedes(T1, T2) means the ending instant of T1 is before the starting instant of T2.
precedesðT 1 ; T 2 Þ $ beforeðendFnðT 1 Þ; startFnðT 2 ÞÞ (b) meets(T1, T2) means the ending instant of T1 is the same as the starting instant of T2.
meetsðT 1 ; T 2 Þ $ endFnðT 1 Þ ¼ startFnðT 2 Þ (c) overlaps(T1, T2) signifies that the starting instant of T1 is before that of T2, the starting instant of T2 is before the ending instant of T1, and the ending instant of T1 is before that of T2. Formally,
overlapsðT 1 ; T 2 Þ $ beforeðstartFnðT 2 Þ; endFnðT 1 ÞÞ ^ beforeðstartFnðT 1 Þ; startFnðT 2 ÞÞ ^ beforeðendFnðT 1 Þ; endFnðT 2 ÞÞ (d) starts(T1, T2) means that the starting instant of T1 is same as that of T2, and the ending instant of T1 is before that of T2. Formally,
startsðT 1 ; T 2 Þ $ ðstartFnðT 1 Þ ¼ startFnðT 2 ÞÞ ^ beforeðendFnðT 1 Þ; endFnðT 2 ÞÞ (e) during(T1, T2) means that the starting instant of T1 is after that of T2, and the ending instant of T1 is before that of T2. Formally,
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duringðT 1 ; T2 Þ $ beforeðstartFnðT 2 Þ; startFnðT 1 ÞÞ ^ beforeðendFnðT1 Þ; endFnðT2 ÞÞ (f) finishes(T1, T2) means that the starting instant of T1 is before that of T2, and the ending instant of T1 is same as that of T2. Formally,
finishesðT 1 ; T 2 Þ $ ðendFnðT1 Þ ¼ endFnðT2 ÞÞ ^ beforeðstartFnðT1 Þ; startFnðT 2 ÞÞ (g) equals(T1,T2) denotes that the starting instant of T1 is the same as that of T2, and the ending instant of T1 is the same as that of T2. Formally,
equalsðT 1 ; T 2 Þ $ ðstartFnðT 1 Þ ¼ startFnðT 2 ÞÞ ^ ðendFnðT 1 Þ ¼ endFnðT 2 ÞÞ (6) We will give axioms about relating an event with an instant or interval. First, at-instant(e, t) means that an event e occurs at an instant t. Now, we define four predicates for events occurring during intervals. The predicate cc-during(e, T) shows e occurs continuously during an interval T, including its starting and ending instants1. We also use other three relevant predicates: oo-during(e, T), oc-during(e, T) and co-during(e, T), depending on whether e occurs at the starting and ending instants of T. For example, co-during(e, T) means that e occurs at every instant of T, including its starting instant but excluding its ending instant. (a) "e "T (cc-during(e, T) M "t (inside(t, T) ? at-instant(e, t))) (b) "e"T (oc-during(e, T) M "t (inside(t, T) ^ t – startFn(T) ? at-instant(e, t))) (c) "e"T (co-during(e, T) M "t (inside(t, T) ^ t – endFn(T) ? at-instant(e, t))) (d) "e"T (oo-during (e, T) M "t (inside (t, T) ^ t – startFn(T) ^t – endFn(T) ? at-instant(e, t)))
3.2.2. The timing system and the Gregorian timing system A timing system S consists of the following ingredients: (1) A language L; (2) Axioms about calendar intervals and instants; (3) Temporal entities and terms expressing those entities. A language L for S is a triple (U, O, F), where (1) a set U of units for time instants and intervals; (2) a set O of operations. We assume that first and last are two built-in operations such that given a string r of symbols, first(r) is the first symbol of r, last(r) is the last symbol of r. (3) a set F of functions. durationFn(T, u) is the amount of time within an interval T as measured in a unit u. For instance, U in the Gregorian timing system is given below.
U ¼ fðcenturyÞ; ðdecadeÞ; ðyearÞ; ðmonthÞ; ðweekÞ; ðdayÞ; ðhourÞ; ðminuteÞ; ðsecondÞg: As an example, a string r = ‘‘2008(year)08(month)08(day)20 (hour)08(minute)00(second)” is a term in this timing system, simply denoted by ‘‘2008:08:08:20:08:00” in the international standard time notation2, and first(r) = (year), last(r) = (second). 1 Note that cc- means that the left-closure and right-closure of T are counted in; that is, the event also occurs at both the starting and ending instants of T. This explanation is applicable to oc-, co- and oo-, where o means the event does not occur at the corresponding instant. 2 http://www.cl.cam.ac.uk/~mgk25/iso-time.html.
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In the following we will give axioms about calendar intervals and instants in the Gregorian timing system. We use the predicate solar-year(x) to show that x is an instance of the class Solar Year, month(x, m) to denote that x is an instance of the class of the mth Month, and the function successorFn(x, u) to be the successor of x in a time unit u. For example, if y = successorFn(1, month), then month(y, 2) holds. Here, t4 is an instant of 0:00 on the solar day when the sun returns to the Vernal Equinox, t5 is an instant of 24:00 on the solar day before the solar day on which the sun returns to the Vernal Equinox next time, and ‘‘” is the logical operator exclusive or. (a) solar-year(x) ? (startFn(x) = t4) ^ (endFn(x) = t5) ^ ((durationFn (x, day) = 365) (durationFn(x, day) = 366)) (b) month(x, 1) ? "y(solar-year(y) ^ contains(y, x) ? startFn(x) = startFn(y)) (c) month(x, 12) ? "y(solar-year(y) ^ contains(y, x) ? endFn(x) = endFn(y)) (d) month (x, m) ^ (y = successorFn(x, month)) ? "z(solar-year(z) ^ contains(z, x) ^ contains(z, y) ? endFn(x) = startFn(y)) (e) month (x, 1) _ month (x, 3) _ month(x, 5) _ month(x, 7) _ month (x, 8) _ month(x, 10) _ month(x, 12) ? durationFn(x, day) = 31 (f) month(x, 2) ? (durationFn(x,day) = 28) (durationFn(x, day) = 29) (g) month(x, 4) _ month(x, 6) _ month(x, 9) _ month(x, 11) ? durationFn(x, day) = 30 Predicates decade(x) and century(x) say that x is an instance of the class of Decade and Century, respectively. Axioms about decades and centuries are given as follows. Here, t6 and t8 are instants of 0:00 on the first solar day of the solar year which can be divided exactly by 10 and 100, respectively; t7 is an instant of 24:00 on the last solar day of the solar year that is the sum of the starting solar year of the decade and 9; t9 is an instant of 24:00 on the last solar day of the solar year that is the sum of the starting solar year of the decade and 99. (a) decade(x) ? (startFn(x) = t6) ^ (endFn(x) = t7) ^ (durationFn(x, year) = 10) (b) century(x) ? (startFn(x) = t8) ^ (endFn(x) = t9) ^ (durationFn(x, year) = 100) For example, axioms below reflect relations between some time units. (a) 60 durationFn(T, hour) = durationFn (T, minute) (b) 24 durationFn (T, day) = durationFn (T, hour) (c) 12 durationFn (T, year) = durationFn (T, month) What time an instant is in is relative to the time zone. For example, if the local time was 9:00 on January 2, 2010 in Beijing located in the 8th Eastern Time Zone, then the local time was 21:00 on January 1, 2010 in Washington located in the 5th Western Time Zone. Predicate time-of(t; y, m, d, h, n, s; z) is defined for this, where y, m, d, h, n and s are integers, 1 6 m 6 12, 1 6 d 6 31, 0 6 h 6 24, 0 6 n 6 60, 0 6 s 6 60, and z is a world time zone. Axiom (a) below states the relations between times in different time zones. Axiom (b) shows a method of computing the duration of an interval T whose starting and ending instants are in different time zones. Here, durationof(T, Dy, Dm, Dd, Dh, Dn, Ds) denotes that the duration of T is Dy years, Dm months, Dd days, Dh hours, Dn minutes, and Ds seconds, and the values of these six arguments are real numbers. (a) time-of(t; y, m, d, h, n, s; GMT) M time-of(t; y, m, d, h x, n, s; the xth western time zone) ^ time-of(t; y, m, d, h + x, n, s; the xth eastern time zone) ^ (1 6 x 6 12)
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(b) "T "t1 "t2 ((startFn(T) = t1) ^ (endFn (T) = t2) ^ time-of(t1; y1, m1, d1, h1, n1, s1; z) ^ time-of(t2; y2, m2, d2, h2, n2, s2; z) ? durationof(T; y1 y2, m1 m2, d1 d2, h1 h2, n1 n2, s1 s2)) 3.2.3. The timing ontology This subsection will introduce the components of the timing ontology: classes of temporal entities, attributes of classes, and relationships between classes, and formal semantic axioms. We first give some basic definitions. Definition 1. Given a class C1 and its instance I1, the property space of I1 is the set of all properties that I1 satisfies, written as proins(I1); the property space of C1 is the set of common properties of all instances of C1, written as procla(C1). For example, procla(Precise Temporal Entity) is a set of common properties of all instances of the class of Precise Temporal Entity, where these instances (e.g. from A.D.2000 to A.D.2010) have the unique starting and ending instants. Definition 2. Given two classes C1 and C2, if procla(C1) procla(C2), we say that C2 is a subclass of C1, and C1 is a super-class of C2. Definition 3. Given a class C and its subclasses SC1, SC2, . . . , SCn, an instance I of C, if the following formula holds, then we say that the classification {SC1, SC2, . . . , SCn} of C is a partition of C, where i, j and n are natural numbers, 1 6 i, j 6 n.
8i8j ðði–jÞ ! :9IðproinsðIÞ proclaðSC i Þ [ proclaðSC j ÞÞÞ ^ð
n \
proclaðSC i Þ ¼ proclaðCÞÞ
i¼1
() :9IðproinsðIÞ ðproclaðSC 1i Þ [ proclaðSC 2p ÞÞ [ ðproclaðSC 1j Þ [ proclaðSC 2q ÞÞÞ () :9IðproinsðIÞ ððproclaðSC 1i Þ [ proclaðSC 1j ÞÞ [ ðproclaðSC 2p Þ [ proclaðSC 2q ÞÞÞÞ Since {SC11, SC12, . . . , SC1n} and {SC21, SC22, . . . , SC2m} are two partitions of C1, then the following two formulas hold based on the definition of the partition.
8i8jðði–jÞ ! :9IðproinsðIÞ proclaðSC 1i Þ [ proclaðSC 1j ÞÞÞ 8p8qððp–qÞ ! :9IðproinsðIÞ proclaðSC 2p Þ [ proclaðSC 2q ÞÞÞ: Hence, we get the formula below.
8i8j8p8qðði – jÞ ^ ðp – qÞ ! :9IðproinsðIÞ ðproclaðSC 1i Þ [ proclaðSC 1j ÞÞ [ ðproclaðSC 2p Þ [ proclaðSC 2q ÞÞÞÞ That is, 8i8j8p8qððip – jqÞ ! :9IðproinsðIÞ proclaðCC ip Þ[ proclaðCC jq ÞÞÞ: (4) Because {SC11, SC12, . . . , SC1n} and {SC21, SC22, . . . , SC2m} are T two partitions of C1, then we obtain ni¼1 proclaðSC 1i Þ ¼ proclaðC 1 Þ Tm and j¼1 proclaðSC 2j Þ ¼ proclaðC 1 Þ. Furthermore,
proclaðCC 11 Þ \ \ proclaðCC 1m Þ \ \ proclaðCC n1 Þ \ \ proclaðCC nm Þ () ðproclaðSC 11 Þ [ proclaðSC 21 ÞÞ \ \ ðproclaðSC 11 Þ [ proclaðSC 2m ÞÞ \ \ ðproclaðSC 1n Þ [ proclaðSC 21 ÞÞ \ \ ðproclaðSC 1n Þ [ proclaðSC 2m ÞÞ () ðproclaðSC 11 Þ [ ðproclaðSC 21 Þ \ \ proclaðSC 2m ÞÞÞ \ ðproclaðSC 12 Þ [ ðproclaðSC 21 Þ \ \ proclaðSC 2m ÞÞÞ \ \ ðproclaðSC 1n Þ
Definition 4. Given a class C1 and its subclasses SC1, SC2, and a class C2, if the following formula holds, then we say that C2 is an intersection of class of SC1 and SC2.
proclaðSC 1 Þ [ proclaðSC 2 Þ ¼ proclaðC 2 Þ According to definitions of the subclass and the intersection of class, we can deduce Theorem 1 below. Based on the definitions of the partition and the intersection of class, we can infer Theorem 2. Theorem 1. Given a class C1 and its subclasses SC1 and SC2, if C2 is an intersection of class of SC1 and SC2, then C2 is a subclass of C1. Proof. If C2 is an intersection of class of SC1 and SC2, then procla S (SC1) procla(SC2) # procla(C2) holds based on the definition of the intersection of class. Since SC1 and SC2 are subclasses of C1, then procla (C1) procla(SC1) and procla(C1) procla(SC2) hold according to the definition of the subclass. Further, we have procla(C1) procla(C2), that is, C2 is a subclass of C1. h Theorem 2. Given two partitions {SC11, SC12, . . . , SC1n} and {SC21, SC22, . . . , SC2m} of C1, if 8i8jðproclaðCC ij Þ ¼ proclaðSC 1i Þ [ procla ðSC 2j ÞÞ, then {CC11, CC12, . . . , CC1m, CC21, . . . , CC2m, . . . , CCn1, . . . , CCnm} is a partition of C1, that is, the set of all intersection of classes of these two partitions is a partition of C1. Proof. (1) Based on Theorem 1, we get that CC11, . . . , CC1m, CC21, . . . , CC2m, . . . , CCn1, . . . , CCnm are subclasses of C1. (2) For any two intersection of classes CCip and CCjq (1 6 i, j 6 n, 1 6 p, q 6 m), we have
:9IðproinsðIÞ proclaðCC ip Þ [ proclaðCC jq ÞÞ
[ ðproclaðSC 21 Þ \ \ proclaðSC 2m ÞÞÞ () ðproclaðSC 11 Þ \ proclaðSC 12 Þ \ \ proclaðSC 1n ÞÞ [ ðproclaðSC 21 Þ \ proclaðSC 22 Þ \ \ proclaðSC 2m ÞÞ () proclaðC 1 Þ [ proclaðC 1 Þ () proclaðC 1 Þ According to the definition of the partition, we can infer that {CC11, CC12, . . . , CC1m, CC21, . . . , CC2m, . . . , CCn1, . . . , CCnm} is a partition of C1. h In this paper, the taxonomy of classes of temporal entities and formal models for these classes are an extension of our previous work [38]. In the work [38], there are four classifications of the class of Temporal Entity (TE): Time TE and Duration, Precise TE and Fuzzy TE, Absolute TE and Relative TE, and Direct TE and Indirect TE. In addition, formal models of TE and these eight subclasses have been constructed in the work [38]. In this paper, we further build a classification of Time TE (shown in Fig. 2) and formal models for eleven subclasses of Time TE. It is pointed out that every classification of each class in this taxonomy is a partition of this class. Time TE is divided into Individual of TE such as ‘‘September.21.2009” and Category of TE such as ‘‘autumn every year” based on whether it denotes a collection of temporal entities with certain common properties. Individual of TE is partitioned into Individual of Time Instant and Individual of Time Interval according to its topological structure. Further, Individual of Time Interval includes Individual of Left Open and Right Open Interval, Individual of Left Closed and Right Open Interval, Individual of Left Open and Right Closed Interval, and Individual of Left Closed and Right Closed Interval in terms of continuity of intervals. For example, ‘‘From 2000 to 2009” is an instance of the last class. Category of TE is segmented into Category of Time Instant and Category of Time Interval based on its topological structure. Category of Time Interval only comprises a subclass of Category of Left Closed and
C. Zhang et al. / Knowledge-Based Systems 24 (2011) 1057–1074
Time Temporal Entity Individual of Temporal Entity Individual of Time Instant Individual of Time Interval Individual of Left Open and Right Open Interval Individual of Left Closed and Right Open Interval Individual of Left Open and Right Closed Interval Individual of Left Closed and Right Closed Interval Category of Temporal Entity Category of Time Instant Category of Time Interval Category of Left Closed and Right Closed Interval hyponymy Relationship Fig. 2. The taxonomy of time temporal entity.
Right Closed Interval (e.g. from January to March every year) grounded on continuity of intervals. As illustration, we will give the model for the class of Category of Left Closed and Right Closed Interval. This class possesses four attributes: value, modifier, number of the set of discontinuous intervals, and duration length. The set of discontinuous intervals means that any two intervals T1 and T2 in this set satisfy precedes(T1, T2) or precedes(T2, T1). Axioms are classified into four types based on objects they describe: axioms of memberships of classes, properties of attributes, relationships between attributes, and relationships between classes [38]. Examples of each type of axioms are given below: (a) category-of-lcrc-interval(T) M $k((T = T1 [ T2 [ [Tk) ^ (k > 1) ^ "i((1 6 i 6 k) ^ individual-of-lcrc-interval(Ti)) ^ "i((1 6 i < k) ^ before(endFn(Ti), startFn(Ti+1)))) (b) category-of-lcrc-interval(T) ? (number-of-disc-intervalFn(T) > 1) (c) category-of-lcrc-interval(T) ^ $k((k = number-of-disc-intervalFn (T)) ^ (T = T1[ [Tk) ^ "i((1 6 i 6 k) ^ individual-of-lcrc-interval(Ti))) ? "u(durationFn(T, u) = durationFn(T1, u) + . . . + durationFn(Tk, u)) (d) time-temporal-entity(x) M (individual-of-temporal-entity(x) ^ : category-of-temporal- entity(x)) _ (:individual-of-temporal-entity (x) ^ category-of-temporal-entity(x)) Axiom (a) means that T is an instance of Category of Left Closed and Right Closed Interval if and only if T is composed of at least two discontinuous intervals which are instances of Individual of Left Closed and Right Closed Interval. Axiom (b) says that the number of discontinuous intervals of T is greater than one. Axiom (c) expresses that the duration length of T is equal to the sum of duration lengths of discontinuous intervals included in T. Axiom (d) represents relations between Time TE and its two subclasses: Individual of TE and Category of TE. Here, function number-of-disc-intervalFn(T) is the number of discontinuous intervals included in T, predicate time-temporal-entity(x) denote that T is an instance of Time TE, and predicates individual-of-temporal-entity(x), individual-of-lcrc-interval(T), category-of-temporal-entity(x), and category-of-lcrc-interval(T) have the analogous meanings.
3.3. Other parts of the Chinese time ontology With the construction of the base time ontology, another task in developing the Chinese time ontology is to build formal models for temporal measurement and representation in Chinese ways, and transformation methods between temporal entities in the Gregorian timing system and those in the traditional Chinese timing system. First we need to mention one point: whether a temporal
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entity is an instant or interval is generally a pragmatic question. For example, we could consider the date ‘‘January 1, 2010” as an instant, and say that an event occurs on that day; or we could consider the date as an interval, and say that an event occurs during that day. 3.3.1. The traditional Chinese timing system We first introduce 24 Solar Terms, which are the basis of setting lunar years and lunar months, and the unique timing method in the world. The 24 Solar Terms divide the ecliptic into 24 equal segments, with 15 of the Sun’s longitude between two terms. Solar terms of even degrees are called major solar terms. The 24 Solar Terms reflect seasonal alternations, weather changes, agricultural activities, etc., and play a significant role in ordinary life and activities. In the traditional Chinese timing system, the set of time units is {(Hua-jia(花甲 in Chinese)), (Ji(纪 in Chinese)), (Lunar Year), (Lunar Month), (Lunar Day), (Shi-chen(时辰 in Chinese)), (Geng (更 in Chinese))} (see Appendix for Chinese terms and their explanations). As a calendar interval, a time unit u has its specific starting instant, ending instant and duration length L. In contrast, when it acts as a duration, it is any interval whose duration length is L. (a) A Hua-jia is a cycle of sixty consecutive lunar years. It starts from the Jia-zi(甲子 in Chinese) lunar year, and ends in the Gui-hai (癸亥 in Chinese) lunar year. (b) A Ji is only used as an instance of Duration, and is any interval whose duration length is 12 lunar years, not as an instance of Time TE. (c) A lunar year is a period of time having 12 lunar months. (d) A lunar month is a period of 29 or 30 days. (e) A lunar day is a period of time having 24 h. A day in the traditional Chinese calendar is different from one in the Gregorian calendar in starting and ending instants, as shown in axiom (a) and (b) below. For distinguishing days in two calendars, we use a lunar day for a day in the traditional Chinese calendar. (f) A Shi-chen or a Geng is a period of time having 2 h. We introduce predicates common-lunar-year(x) and leap-lunaryear(x) to denote x is an instance of the class of Common Lunar Year, and Leap Lunar Year, respectively. Predicates lunar-month(x), lunarday(x), hua-jia(x), ji(x), shi-chen(x), and geng(x) have the analogous meanings. We use t10 for a starting instant on the new moon lunar day, t11 for an ending instant on the lunar day before the next new moon lunar day, t12 for a starting instant on the first lunar day of the lunar month which contains the solar term Spring Showers, t13 for an ending instant on the lunar day before the first lunar day of the lunar month which contains the next Spring Showers, t14 for a starting instant on the first lunar day of the Jia-zi lunar year, and t15 for an ending instant on the last lunar day of the Gui-hai lunar year. (a) solar-day(x) ? (startFn(x) = 0:00 on the day x) ^ (endFn(x) = 24:00 on the day x) ^ (durationFn(x, hour) = 24) (b) "x "y "T(lunar-day(x) ^ solar-day(y) ^ (startFn(x) = startFn (T)) ^ (startFn(y) = endFn(T)) ^ (durationFn(T, hour) = 1) ? (startFn(x) = 23:00 on the solar day before the solar day y) ^ (endFn (x) = 23:00 on the solar day y) ^ (durationFn(x, hour) = 24)) (c) lunar-month(x) ? ((startFn(x) = t10) ^ (endFn (x) = t11)) ^ ((durationFn(x, lunar day) = 29) (durationFn(x, lunar day) = 30)) (d) common-lunar-year(x) ? ((startFn(x) = t12) ^ (endFn (x) = t13)) ^ (durationFn(x, lunar month) = 12) (e) leap-lunar-year(x) ? durationFn(x, lunar month) = 13 (f) hua-jia(x) ? (startFn(x) = t14) ^ (endFn (x) = t15) ^ (durationFn (x, lunar year) = 60) (g) ji(x) ? durationFn(x, lunar year) = 12 W (h) shi-chen(x) geng(x) ? durationFn(x, hour) = 2
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3.3.2. Representation and transformation of lunar years This subsection will introduce three representing systems for lunar years and transformation between lunar years and solar years. These systems are: the Stem-Branch System, the Animal Sign System, and the Emperor’s Title and Reign Title System. 3.3.2.1. The Stem-Branch System for lunar years representation. The Stem-Branch System has been used as a principal timing method since ancient times [40]. The system is composed of the ten sequential celestial stems (Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui) and the twelve sequential terrestrial branches (Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai) as shown in Table 1. The system is a totally ordered set of the 60 ordered combinations of celestial stems and terrestrial branches (called stembranch combinations). Table 1 lists those 60 ordered combinations, and the number indicates the index of each combination. For example, the first combination is Jia-zi, which consists of the first celestial stem Jia and the first terrestrial branch Zi. The second combination is Yi-chou, which consists of the second celestial stem Yi and the second terrestrial branch Chou. Those sixty stem-branch combinations express a cycle of 60 lunar years. For instance, A.D.1924, A.D.1984, A.D.2044 and so on are called the Jia-zi Lunar Year, and are instances of the class of Jia-zi Lunar Year, while A.D.1925, A.D. 1985, A.D.2045 and so on are called the Yi-chou Lunar Year. The period from A.D.1924 to A. D.1983 is a complete cycle, so is from A.D.1984 to A.D.2043. Note that, due to the circularity of the sixty stem-branch combinations, each combination actually denotes a class of lunar years. 3.3.2.2. The Animal Sign System for lunar years representation. The 12 Animal Sign System is a totally ordered set of the 12 ordered animal signs, and is used to represent a cycle of 12 lunar years. The first and second rows in Table 2 show the 12 animal signs and their orders. Each animal sign corresponds to a fixed terrestrial branch (shown in Table 2), and denotes a class of lunar years with an identical terrestrial branch. For example, A.D.1984, A.D.1996 and A.D.2008 are called the Rat Lunar Year, and are instances of
the class of Rat Lunar Year, and they all correspond to the first terrestrial branch (Zi). 3.3.2.3. The emperor’s title and reign title system for lunar years representation. In Chinese history, most emperors used their titles or reign titles to express lunar years. Each emperor in a dynasty started counting lunar years by his or her first year of reign as the first lunar year of using the emperor’s title or reign titles. For instance, the title of emperor Ai-xin-jue-luo Min-ning(爱新觉罗旻 宁 in Chinese) in the Qing Dynasty (清朝 in Chinese) is Xuan-zong (宣宗 in Chinese) during his rule from A.D.1821 to A.D.1850, so A. D.1821 is called the first lunar year of the Emperor Xuan-zong Aixin-jue-luo Min-ning of the Qing Dynasty. Let Sd is the set of all dynasties, Sep is the set of all emperors, Sty be the set of {Title, Reign Title}, Set is the set of titles or reign titles of all emperors, Sy is the set of solar years, and N is the set of natural numbers. We introduce three functions below. These functions are to obtain the starting solar year, the ending solar year, and the nth solar year of the title or reign title et of the emperor ep in the dynasty d, and ty denotes the type of et. We have the axiom TCT1. (a) starting-solar-yearFn(ty, ep, et, d): Sty Sep Set Sd ? Sy. (b) ending-solar-yearFn(ty, ep, et, d): Sty Sep Set Sd ? Sy. (c) nth-title-solar-yearFn(ty, n, ep, et, d): Sty N Sep Set Sd ? S y. TCT1. (starting-solar-yearFn(ty, ep, et, d) = sy1) ^ ^ (ending-solaryearFn(ty, ep, et, d) = sy2) ? (nth-title-solar-yearFn(ty, n, ep, et, d) = sy1 + n 1) ^ (1 6 n 6 sy2 sy1 + 1) For emperor Ai-xin-jue-luo Min-ning of the Qing Dynasty, we have the following facts. (a) starting-solar-yearFn(Title, Ai-xin-jue-luo Min-ning, Xuanzong, Qing) = A.D.1821. (b) ending-solar-yearFn(Title, Ai-xin-jue-luo Min-ning, Xuanzong, Qing) = A.D.1850.
Table 1 The 60 ordered combinations of celestial stems and terrestrial branches in the stem-branch system.
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Animal sign Terrestrial branch
1
2
3
4
5
6
7
8
9
10
11
12
Rat Zi
Ox Chou
Tiger Yin
Rabbit Mao
Dragon Chen
Snake Si
Horse Wu
Sheep Wei
Monkey Shen
Rooster You
Dog Xu
Pig Hai
(c) nth-title-solar-yearFn(Title, n, Ai-xin-jue-luo Min-ning, Xuanzong, Qing) = A.D.(1821 + n 1), where 1 6 n 6 30.
3.3.2.4. Transformation between lunar years and solar years. In the following, we discuss transformation methods between solar years and lunar years. First, we introduce some functions and predicates. (1) In order to use our Chinese time ontology practically, an instant t is required to be identifiable. For example, (a) if t refers to a solar/lunar month, then the solar/lunar year which the month belongs to is specified in t; (b) if t refers to a solar/lunar day, then both the solar/lunar year and month which the day belongs to is also specified in t. Based on this, we introduce functions yearFn(t, sl1), monthFn(t, sl1), dayFn(t, sl1), hourFn(t, sl2), and shi-chenFn(t, sl3), where sl1 e {solar, lunar}, sl2 e {solar}, and sl3 e {lunar}. The ranges of these five functions are the sets of all representations of the solar/lunar year, month, day, hour, and Shi-chen which t belongs to, respectively. (2) last-lunar-dayFn(ly, lm) is a function which gets the index of the last lunar day of the lunar month lm in the lunar year ly. Here, ly and lm are representations for lunar years and lunar months, respectively. (3) The function modFn(x, n) calculates the remainder of an integer x divided by a positive integer n, and 0 6 modFn(x, n) < n. (4) Let v belongs to the set {lunar year, lunar month, lunar day, Shi-chen}, the predicate stem-branch-no(t, v, n) means that the stem-branch combination representation of v to which t belongs is the nth index of the Stem-Branch System. Accordingly, we define predicates celestial-stem-no(t, v, n) and terrestrial-branch-no(t, v, n). (5) Predicate stem-branch-combination(sb, s, b) is true when the sth celestial stem and the bth terrestrial branch constitute the sbth stem-branch combination. As shown in Table 1, not all combinations of celestial stems and terrestrial branches are meaningful in the Stem-Branch System. In fact, they must satisfy TCT2 below. TCT2. "sb"s"b(stem-branch-combination(sb, s, b) M (s = 10 modFn(10 sb, 10) ^ b = 12 modFn(12 sb, 12))) For a given temporal entity in the Gregorian timing system, we often need to calculate its corresponding temporal entity in the traditional Chinese timing system and vice versa. First, we consider mapping relationships between solar years and lunar years. This calculation is given in TCT3, TCT4, TCT5 and TCT6 below, where k is an integer. TCT7 is used to calculate the celestial stem and the terrestrial branch representations for a solar year. TCT3. "t "y(before(A.D.1, t) ^ y = yearFn(t, solar) ? stem-branch-no(t, lunar year, 60-modFn(3-modFn(y, 60), 60))) TCT4, "t "y(before(t, B.C.1) ^ y = yearFn(t, solar) ? stem-branch-no(t, lunar year, 60- modFn(modFn(y, 60) + 2, 60))) TCT5. "t "x(before(A.D.1, t) ^ stem-branch-no(t, lunar year, x)
? yearFn(t, solar) = 60k + x 57) TCT6. "t"x(before(t, B.C.1) ^ stem-branch-no(t, lunar year, x) ? yearFn(t, solar) = 60k x + 58) TCT7. "t "m(stem-branch-no(t, lunar year, m) ? celestial-stem-no (t, lunar year, 10-modFn(10-m, 10)) ^ terrestrial-branch-no(t, lunar year, 12-modFn(12-m, 12))) As illustration, we calculate the stem-branch combination representation of the solar year A.D.2008 as follows. (a) Since before(A.D.1, A.D.2008) is true and 60 modFn (3 modFn(2008, 60), 60) = 25, stem-branch-no(A.D.2008, lunar year, 25) is true according to TCT3. (b) The 25th stem-branch combination is Wu-zi by referring to Table 1, so we say that A.D.2008 is an instance of the class of Wu-zi Lunar Year. 3.3.3. Representation and transformation of lunar months There are two commonly used methods of expressing lunar months. The first method is based on ordinal numbers, i.e. the first lunar month, . . . , the twelfth lunar month. The second method is based on the Stem-Branch System. The celestial stem of any lunar month of any lunar year can be specified by the celestial stem of this lunar year, and the inference formula is shown in TCT8. For example, if the celestial stem of a lunar year is Jia or Ji, then the celestial stem of the first lunar month in this lunar year is Bing. If the celestial stem of a lunar year that t belongs to is unknown, the celestial stem of a lunar month which t belongs to can be inferred by the solar year that t belongs to, as shown in TCT9. TCT10 and TCT11 are formulas to transform between the terrestrial branch representation of a lunar month and its ordinal number representation. TCT8. "t "lm "n(lm = monthFn(t, lunar) ^ celestial-stem-no(t, lunar year, n) ?celestial-stem-no(t, lunar month, modFn(2 modFn(n, 5) + lm, 10))) TCT9. "t"lm(lm = monthFn(t, lunar) ^ (y = yearFn(t, solar)) ?celestial-stem-no(t, lunar month, modFn(lm + 2 modFn(y, 5) 6, 10))) TCT10. "t "lm(lm = monthFn(t, lunar) ?terrestrial-branch-no(t, lunar month, modFn(lm + 2, 12))) TCT11. "t "x "y(terrestrial-branch-no(t, lunar month, x) ? (y = monthFn(t, lunar)) ^ (y = x + 12k 2) ^ (1 6 y 6 12)) 3.3.4. Representation and transformation of lunar days The four main ways for representing lunar days are the approaches based on ordinal numbers, the Stem-Branch System, the phases of the moon, and the traditional Chinese festivals. The Stem-Branch System for lunar days’ denotation uses the 60 stembranch combinations to express lunar days. This counting method has so far the longest history among the day counting methods in the world. During each lunar month, the moon has several special phases, which are used to represent lunar days. These phases include Shuo (朔 in Chinese, i.e. new moon), Wang (望 in Chinese, i.e. full moon) and Hui(晦 in Chinese, i.e. the last lunar day of a lunar month). For each instant t which involves a phase of the Moon,
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we use the function moon-phaseFn(t) to means the moon phase in which t is. Then we have the following facts about moon phases. (a) (moon-phaseFn(t) = Shuo) M (dayFn(t, lunar) = 1) (b) (moon-phaseFn(t) = Wang) M (dayFn(t, lunar) = 15) (c) (ly = yearFn(t,lunar)) ^ (lm = monthFn(t, lunar)) ^ (moon-phaseFn(t) = Hui) M (dayFn(t, lunar) = last-lunar-dayFn(ly, lm)) The main traditional Chinese festivals have the Spring Festival or the Chinese New Year, the Lantern Festival, the Dragon Boats Festival, the Middle Autumn Festival, the Double Ninth Festival, and the Chinese New Year’s Eve. Function Chinese-festivalFn(t) is used to denote the Chinese festival which t is in. For example, W (Chinese-festivalFn(t) = Spring Festival) (Chinese-festivalFn(t) = Chinese New Year) M (monthFn(t, lunar)=1) ^ (dayFn(t, lunar) = 1) 3.3.5. Representation and transformation of hours There exist three methods of expressing hours of a lunar day: the approaches based on colors of the sky, the terrestrial branch, and the clapper, as shown in Fig. 3. Chinese ancient people averagely divided a lunar day into twelve segments, and each segment is called a Shi-chen. The 12 Shi-chen are named Ye-ban(夜半 in Chinese), Ji-ming(鸡鸣), Ping-dan(平旦), Ri-chu(日出), Shi-shi(食时), Yuzhong(隅中), Ri-zhong(日中), Ri-die(日昳), Bu-shi(晡时), Ri-ru(日入), Huang-hun(黄昏), and Ren-ding(人定), as shown in Fig. 3. These names have meanings relating to the natural law of sunrise and sunset, changes of the sky color, and people’s living customs. For instance, Ji-ming means the time when roosters call, that is, the period from 1:00 am to 3:00 am. As illustration, we give an axiom about Ji-ming, where the function shi-chenFn(t) represents the Shichen that t is in, and SC is the set of 12 Shi-chen. (a) (sc = shi-chenFn(t) ^ sc = Ji-ming) M (startFn(sc) = 1:00 am) ^ (endFn(sc) = 3:00 am) (b) "sc((sc SC) ^ durationFn(sc, hour) = 2) The terrestrial branch is also used to denote Shi-chen. Each Shichen corresponds to a fixed terrestrial branch. For instance, Ji-ming is also called Chou-shi, whose terrestrial branch is Chou. The 12 Shi-chen are sequentially named Zi-shi, Chou-shi, Yin-shi, Mao-shi, Chen-shi, Si-shi, Wu-shi, Wei-shi, Shen-shi, You-shi, Xu-shi, and Hai-shi, as shown in Fig. 3. As an example, an axiom about Ji-ming is (shi-chenFn(t) = Ji-ming) M terrestrial-branch-no(t, shi-chen, 2). Hours can also be represented by the Stem-Branch System. The celestial stem of a Shi-chen is specified by the celestial stem of the lunar day in which the Shi-chen is, as shown in TCT12.
TCT12. "m"n(terrestrial-branch-no(t, shi-chen, m) ^ celestialstem-no(t, lunar day, n) ?celestial-stem-no(t, shi-chen, modFn(2 modFn(n, 5) 1, 10) + modFn(m 1, 10))) For example, let t is in the Shi-chen of Chou-shi on September 21, 2008, the steps of computing the stem-branch combination representation of this Shi-chen are as follows: (a) The stem-branch combination representation of September 21, 2008 is Jia-zi, so celestial-stem-no(September 21, 2008, lunar day, 1) is true. (b) Since t is in the Shi-chen of Chou-shi, terrestrial-branch-no(t, shi-chen, 2) holds. (c) Based on TCT12, we have celestial-stem-no(t, shi-chen, modFn (2 modFn(n, 5) 1, 10) + modFn(m 1,10)) = celestial-stemno(t, shi-chen, modFn(2 modFn(1, 5) -1, 10) + modFn(21,10)) = celestial-stem-no(t, shi-chen, 2). (d) Because the second celestial stem is Yi, the stem-branch combination denotation of the Chou-shi on September 21, 2008 is the Shi-chen of Yi-chou. The approach based on the clapper for hours counting segments an interval from 7:00 pm to 5:00 am on the next lunar day into five consecutive sub-intervals: Yi-geng(the first Geng), Er-geng(the second Geng), San-geng(the third Geng), Si-geng(the fourth Geng) and Wu-geng(the fifth Geng), as shown in Fig. 3. For instance, we give an axiom about Yi-geng, where the function gengFn(t) shows the Geng that t is in.
ðg ¼ gengFnðtÞ ^ g ¼ Yi-gengÞ $ ðstartFnðgÞ ¼ 7 : 00 pmÞ ^ ðendFnðgÞ ¼ 9 : 00 pmÞ As seen from the 12 Shi-chen, Yi-geng, Er-geng, San-geng, Sigeng and Wu-geng correspond to Wu-shi, Hai-shi, Zi-shi, Choushi and Yin-shi, respectively. For example,
8g 8scððg ¼ Yi gengÞ ^ ðsc ¼ Wu shiÞ ! equalðg; scÞÞ 3.3.6. Combined representations of temporal entities In spoken and written Chinese, many temporal expressions use more than one method for representing a temporal entity, and are called combined ones. For example, the lunar year of Jia-zi and Rat utilizes two representing methods of lunar years: the Stem-Branch System and the Animal Sign System. This subsection will discuss various combined representations for different periods of time: lunar years, lunar months, lunar days and hours. Based on the three representing methods of lunar years, there are ten types of combined representations of lunar years, as shown
Fig. 3. The approach based on colors of the sky, the terrestrial branch, and the clapper for hours representation.
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The title of a reigning dynasty
1 2 3 4 5 6 7 8 9 10
p
p p p
Emperor’s title
p p p p
Emperor’s name
Emperor’s reign title p p p p
p p
The ordinal number p p
The stembranch
The terrestrial branch
The Animal Sign
p
p p p
p p p p p p
in Table 3. The first row of Table 3 gives the components of combined representations of lunar years: (1) the title of a reigning dynasty, (2) the emperor’s title, (3) the emperor’s name, (4) the emperor’s reign title, (5) the ordinal number of a lunar year, (6) the stem-branch combination representation for a lunar year, (7) the terrestrial branch representation for a lunar year, (8) the animal sign representation for a lunar year. Information in Table 3 will p be filled using ‘ ’ to indicate that it is a component in a certain kind of combined representations. An example of the seventh type of combined representations is the ninth lunar year of the Da-he reign of Emperor Wen-zong of the Tang Dynasty(唐朝文宗大和九年 in Chinese). It includes (a) the title of a reigning dynasty: the Tang Dynasty; (b) the emperor’s title: Wen-zong; (c) the emperor’s reign title: Da-he; (d) the ordinal number of the lunar year: the ninth lunar year. And its corresponding solar year is A.D.835. Combined representations of lunar months are composed of one of ten kinds of combined representations of lunar years above and one of two kinds of representations of lunar months. For instance, the fourth lunar month of the third lunar year of the Xuan-tong reign (宣统三年四月 in Chinese), whose corresponding solar month is May 1911, contains (a) the emperor’s reign title, i.e., Xuan-tong; (b) the ordinal number of the lunar year, i.e., the third lunar year; (c) the ordinal number of the lunar month, i.e., the fourth lunar month. For combined representations of lunar days, they consist of a combined representation of a lunar year above, and one of eight types of combined representations of a lunar month and a lunar day, as shown in Table 4. As illustration, the full moon day of the third lunar month of the Ding-mao lunar year(丁卯年三月望日 in Chinese) is an example of the third type of combined representations. And it comprises: (a) the stem-branch combination of the lunar year: Ding-mao; (b) the ordinal number of the lunar month: the third lunar month; (c) the moon phase of the day: the full moon day. And its corresponding solar day is April 12, 1987 and other dates. A combined representation of a Shi-chen is composed of a combined representation of a lunar year, a combined representation of a lunar month and a lunar day, and one of three kinds of representa-
tions of Shi-chen. For instance, the Ren-ding Shi-chen of the Geng-zi day of the second lunar month of the second lunar year of the Xuantong reign (宣统二年二月庚子日人定时 in Chinese) means the period from 9:00pm to 11:00 pm on April 5, 1910. It includes (a) the emperor’s reign title: Xuan-tong; (b) the ordinal number of the lunar year: the second lunar year; (c) the ordinal number of the lunar month: the second lunar month; (d) the stem-branch combination of the day: Geng-zi; (e) the color of the sky of the Shi-chen: Ren-ding. 3.3.7. Completeness of transformation approaches With the discussion of transformation between solar years/ months/days/hours and lunar years/months/days/Shi-chen, we must consider a problem: are there formulas to make a conversion between any temporal entity in the Gregorian timing system and any temporal entity in the traditional Chinese timing system? Fig. 4 illustrates transforming relationships between temporal entities expressed by different representing methods. The left part of Fig. 4 shows temporal entities of different periods in the traditional Chinese timing system, while the right part of Fig. 4 gives temporal entities of different periods in the Gregorian timing system. Arrows ‘M’, ‘?’, , and indicate that there is a one-toone mapping, an injective mapping, a surjective mapping and a one-to-many relationship of transformation between two sets of temporal entities on the two ends of arrows, respectively. As illustration, there is a one-to-one mapping of transforming relation between the set of Shi-chen represented by the terrestrial branch system and the set of hours expressed by the ordinal numbers according to formulas in Section 3.3.5. For another example, if S1 and S2 are the sets of lunar days denoted by approaches based on the moon phrases and the ordinal numbers, respectively, then there exists an injective mapping of the converting relation from S1 to S2, in terms of formulas in Section 3.3.4. For the third example, there is a one-to-many transforming relation from the set S3 of lunar years described by the Stem-Branch system to the set S4 of solar years denoted by the ordinal numbers, while there is a surjective mapping of the converting relation from S4 to S3. We can make
Table 4 Eight types of combined representations of lunar days. No.
1 2 3 4 5 6 7 8
Lunar years
Lunar months
One of the 10 kinds of combined representations of lunar years p p p p p p p p
The ordinal number p p p
Lunar days The stembranch
The ordinal number p
The phase of the moon
The traditional Chinese festival
p p p p p
p
The stembranch
p p p
p p p p
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A one-to-one mapping An injective mapping A surjective mapping A one-to-many relation
Lunar Years Represented by the Animals Zodiac System
Temporal Entities in the traditional Chinese Timing System
Lunar Years Represented by the Emperor’s and Reign Title System
Lunar Months Represented by the Stem-Branch System Lunar Days Lunar Days Represented Represented by the Approach by the Approach based on based on Phases Traditional of the Moon Chinese Festivals
Shi-chen Represented by the Approach based on Colors of the Sky
Temporal Entities in the Gregorian Timing system
Lunar Years Represented by the Stem-Branch System
Lunar Months Represented by the Approach based on Ordinal Numbers Lunar Days Represented by the Stem -Branch System
Shi-chen Represented by the Approach based on the Clapper
Solar Years Represented by the Approach based on Ordinal Numbers
Solar Months Represented by the Approach based on Ordinal Numbers
Lunar Days Represented by the Approach based on Ordinal Numbers
Shi-chen Represented by the Terrestrial Branch System
Solar Days Represented by the Approach based on Ordinal Numbers
Hours Represented by the Approach based on Ordinal Numbers
Fig. 4. Transformation relationships between temporal entities expressed by different representing methods.
transformation between solar years and lunar years depicted by the Stem-Branch System in the light of formulas in Section 3.3.2.4. It is noticed that there is neither the accurate formula to make a conversion between a solar month and a lunar month, nor the algorithm to do a transformation between a solar day and a lunar day. Because the mutation and rotation of the moon and the sun are uneven, unstable, and wobbling, the length of a solar month is not always greater than the length of a lunar month, and a lunar month might contain two major solar terms. Two points should be emphasized here. First, the New Year’s Day in the Gregorian calendar does not always coincide with the Chinese New Year’s day (i.e. the Chinese Spring Festival’s day), so the mapping between a solar year and a lunar year is only approximate. For example, the New Year’s Day of 2008 in the Gregorian calendar is January 1, while the Chinese New Year started on February 7, 2008. More precisely, for the period from January 1, 2008 to February 6, 2008, the lunar year that it belongs to is an instance of the class of Ding-hai Lunar Year. However, the lunar year including the period from February 7, 2008 to December 31, 2008 is an instance of the class of Wu-zi Lunar Year. Furthermore, the animal sign of a person, who was born during the first period, is Pig. However, the animal sign of a person who was born during the second period is Rat. The second point is that the Stem-Branch System for lunar years representation was used from the Western Han Dynasty; so later people calculated the stem-branch combination representations of lunar years before that time. 4. Comparison and application of our Chinese time ontology 4.1. Comparison with other time ontologies We use the CommonKADS evaluation framework to compare our Chinese time ontology with current main time ontologies, since the framework is the leading methodology to support structured knowledge engineering [6,29,41]. These ontologies include the DAML ontology of time [18], time ontology in OWL [47], KSL time ontology [44], time ontology in KIF [48], and times and dates in Cyc knowledge base [50].
The DAML Ontology of Time Topological Temporal Relations
Our Chinese Time Ontology
The time System
The Timing System
The Timing Ontology
Measuring Durations The Gregorian Calendar and Clock Describing Times and Durations The IS-A Relation
The Gregorian Timing System
The Traditional Chinese Timing System
Transformation between Temporal Entities The Part-Whole Relation
The Corresponding Relation between Two Time Ontologies
Fig. 5. Comparison of the DAML ontology of time and our Chinese time ontology.
Fig. 5 illustrates the comparison and the corresponding relationships between components of the DAML ontology of time and ones of our Chinese time ontology. The DAML ontology consists of four components: topological temporal relations, measuring durations, the Gregorian calendar and clock, and describing times and durations. Our ontology comprises the time system, the timing system, the timing ontology, the Gregorian timing system, the traditional Chinese timing system, the transformation between temporal entities in the Gregorian timing system and those in the traditional Chinese timing system. The first component in the DAML ontology corresponds to the time system in our base time ontology, and they all depict topological temporal relations between time primitives, and linking time and events. The contents of the other three components are included in the Gregorian timing system within our base time ontology. Tables 5–7 show the comparison between our base time ontology with DAML, OWL, KSL, KIF and Cyc time ontologies in aspects of components, domain knowledge, and concepts and taxonomies. Information in these three tables will be filled using ‘+’ to indicate that it is a supported feature in the time ontology, ‘’ for non supported features. In Table 5, all six time ontologies define topological temporal relations, the Gregorian calendar and clock, and times
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C. Zhang et al. / Knowledge-Based Systems 24 (2011) 1057–1074 Table 5 Comparison of components within six time ontologies.
Topological temporal relations Durations measure The Gregorian calendar and clock Times and durations description The timing system The timing ontology
The DAML ontology of time
Time ontology in OWL
KSL time ontology
Time ontology in KIF
Times and dates in Cyc
Our base time ontology
+ + + +
+ + + +
+ + + +
+ + + +
+ + +
+ + + + + +
Table 6 Comparison of main components of domain knowledge in six time ontologies.
Concepts Hyponymy relations Functions Instances Axioms Axioms of membership of concepts Axioms of properties of attributes Axioms of relations between attributes Axioms of relations between concepts
The DAML ontology of time
Time ontology in OWL
KSL time ontology
Time ontology in KIF
Times and dates in Cyc
Our base time ontology
+ + + +
+ + + +
+ + + +
+ +
+ + + +
+ + + +
+ + + +
Table 7 Comparison of concepts and taxonomies in six time ontologies.
Components including temporal concepts Notations for sets of temporal concepts Cardinalities of sets of temporal concepts Relations between sets
Disjoint decompositions Subclass partitions Criterions for concept classification
The DAML ontology of Time
Time ontology in OWL
KSL time ontology
Time ontology in KIF
Times and dates in Cyc
Our base time ontology
Topological temporal relations Sd
Topological temporal relations Sw
KSL time ontology Sk
Times and dates in Cyc Sc
The time system Ss
The Timing Ontology So
3
5
14
7
3
23
Sw Sd
|Sk \ Sd| = 2 |Sk \ Sw| = 2
|Sc \ Sd| = 2 |Sc \ Sw| = 2 |Sc \ Sk| = 2
Ss = Sd
+ +
+
+
+
+ + +
|So \ Sd| = 3 |So \ Sw| = 3 |So \ Sk| = 6 |So \ Sc| = 2 + + +
and durations description. Duration measure is included in four time ontologies excepting KSL and Cyc. The timing system and the timing ontology are only built in our base time ontology. Table 6 indicates the main components of domain knowledge: concepts (i.e. classes of temporal entities), hyponymy relations, functions, instances, and axioms. All six time ontologies support definitions of functions and instances, while five ontologies other than KIF give concepts and their hyponymous relations. It is mentioned that axioms about concepts and attributes are only specified in our base time ontology, and these axioms are given in Section 3.2.3. Fig. 6 gives temporal concepts and their taxonomies in the DAML, OWL, KSL, and Cyc time ontologies. Table 7 summarizes the most important features to be analyzed when describing concepts and taxonomies in an ontology: cardinalities of sets of temporal concepts, relations between these sets, disjoint decompositions, subclass partitions, and criterions for concept classification. The feature of disjoint decompositions means that (a) there may be an instance I1 of a concept C, I1 is not an instance of any sub-concepts of C for a classification; (b) there does not exist an instance I2 of C, I2 is an instance of more than one sub-concept of C for a classification. This feature is supported by five ontologies excepting KIF. Taxonomies in the DAML and our base time ontologies satisfy the property of subclass partitions. Only our base time ontology provides explicit criterions for every classification of each concept.
In brief, the comparison measurement among our base time ontology, DAML, OWL, KSL, KIF, and Cyc time ontologies focuses on components and domain knowledge. The comparison measurement of domain knowledge includes eight features: concepts, hyponymy relations, functions, instances, and axioms about membership of concepts, properties of attributes, relations between attributes, and relations between concepts. Further, the comparison about concepts and taxonomies consists of five features: cardinalities of sets of temporal concepts, relations between these sets, disjoint decompositions, subclass partitions, and criterions for concept classification. In conclusion, the main differences between present time ontologies and our time ontology are given as follows based on the above comparison. (a) The key difference is that we propose the time system, the timing system and the timing ontology to compose the base time ontology. (b) Formal axioms are an indispensable component in our timing ontology. However, other ontologies do not provide formal semantic axioms for temporal entities and their properties. Axioms can be used for constraining the interpretation and use of temporal concepts and their relationships. (c) In contrast with the representation of temporal entities in the Gregorian timing system, there are a variety of representing methods for different kinds of temporal entities in the traditional Chinese timing system. We analyzed these approaches, and built
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The DAML Ontology of Time Temporal Entity Instant Interval
Temporal Entity Time Ontology in OWL Instant Interval Proper Interval Date Time Interval
Time Granularity Time interval Time Point
Temporal Thing Convex Time Interval Temporal Quantity Calendar Month Temporal Stuff Type Non-Convex Time Interval Time Interval Regular Non-Convex Time Interval Temporal Object Type Calendar Day Temporally Disjoint Temporal Object Type Left Open Interval Time Instant Right Open Interval Time Interval Open Right Open Interval Right Close Interval Time Interval Closed Times and Dates in Cyc
KSL Time Ontology
Fig. 6. Temporal concepts and their taxonomies in four time ontologies.
constitutive methods of combined representations of temporal entities. In particular, we have constructed the formulas in the first-order predicate calculus for transformation between temporal entities in the Gregorian and the traditional Chinese timing systems. We aim to provide a method for developing models of temporal measurement, representation, and transformation based on different calendars. 4.2. Applications of our chinese time ontology This subsection will illustrate an application of time ontologies to question answering. We will show which types of questions could be answered by our Chinese time ontology but could not be completed by DAML [18], OWL [47], KSL [44], KIF [48], and Cyc time ontologies [50]. This application is built up on our developed question answering system (QA system) with a Chinese encyclopedic knowledge base [5,8,9,36]. This knowledge base covers twenty-one domains such as medicine, biology, history, geography, mathematics, and archaeology. It comprises more than 3,000,000 assertions, and more than one thousand temporal attributes such as Geological Age of the concept Archaeological Site and Manufacturing Time of the concept Ancient Firearm. Our QA system consists of four major components: a natural language user interface, an encyclopedic knowledge base, domain-specific multi-agent systems for answering and reasoning about users’ questions, and a multi-agent communication protocol [5,8,9]. Each agent represents a class of entities, includes axioms, theorems, and properties rules about this class of entities as its rule base for making inferences, and shares the encyclopedic knowledge base. When our QA system receives a question from a user,
it will take the following main steps to generate the answer. First, it transforms a question in a natural language into a formula represented in the first-order predicate calculus. Second, it calls the agents which represent the classes of entities, and judge whether these classes or their instances are involved in the question. Third, these called agents search the encyclopedic knowledge base and their rule bases, and perform forward or backward reasoning until inferring the answer or completing the searching process. In experiments, we give five types of questions to illustrate the capability of our Chinese time ontology and other time ontologies in question answering. Specially, these questions cover five issues about topological temporal relations, the taxonomy of classes of temporal entities, axioms of temporal entities, the representation of temporal entities, and the transformation between temporal entities in different timing systems. Table 8 lists the types of the questions, examples of those questions, and their answers. As can be seen from Table 8, only the first type of questions could be completed by DAML, OWL, KSL, KIF, and Cyc time ontologies, while all types of questions could be answered by using our Chinese time ontology. The details of how our Chinese time ontology is employed to answer these questions are described as follows. (1) An example of the first type of questions is ‘‘Whether was Karl Heinrich Marx born earlier than Mao Ze-dong(毛泽东 in Chinese)?”, and our QA system answered ‘‘Yes”. There are three steps for answering this question. (a) Our QA system transformed this question into the formula ? Birth-time-earlier-than(Karl Heinrich Marx, Mao Ze-dong), where ‘‘?” means the question is a general question.
Table 8 Examples of types of questions and answers. No.
Types of questions
Questions
Answered by DAML, OWL, KSL, KIF, or Cyc Ontologies
Answers
1
Topological Temporal Relations
Yes
Yes
2
Taxonomy of Classes of Temporal Entities
No
3
Axioms of Temporal Entities
No
Temporal Entity, Absolute Temporal Entity, Precise Temporal Entity 96 hours
4
Representation of Temporal Entities
No
A.D.1740
5
Transformation between Temporal Entities in Different Timing Systems
Whether was Karl Heinrich Marx born earlier than Mao Ze-dong? Whose subclasses include the Absolute and Precise Temporal Entity? What is the temporal length of every Thursday in August 2010? Which solar year is the fifth lunar year of the Qian-long Reign? Which lunar year in the sixty year cycle is A.D.2010?
No
Geng-yin Lunar Year
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(b) Then, the QA system called the agent ‘‘Person-Agent”, since Karl Heinrich Marx and Mao Ze-dong are instances of the class of Person. This agent searched the knowledge about birth times of Mao Ze-dong and Karl Heinrich Marx, and obtained the assertions ‘‘Mao Ze-dong was born in A. D.1893”, ‘‘Karl Heinrich Marx was born earlier than Vladimir Ilich Lenin”, and ‘‘Vladimir Ilich Lenin was born in A.D.1870”. They are represented as Birth-time(Mao Ze-dong, A.D.1893), Birth-time-earlier-than(Karl Heinrich Marx, Vladimir Ilich Lenin), and Birth-time(Vladimir Ilich Lenin, A.D.1870) in the knowledge base, respectively. Further, this agent deduced Birth-time-earlier-than(Vladimir Ilich Lenin, Mao Ze-dong). (c) The agent ‘‘Person-Agent” got the assertion that the relation ‘‘Birth-time-earlier-than” is an instance of the before relation in its rule base. And this agent inferred that this relation satisfies the transitiveness, because it inherits the transitiveness of the before relation in the time system. Hence, this agent derived Birth-time-earlier-than(Karl Heinrich Marx, Mao Ze-dong), i.e. ‘‘Karl Heinrich Marx was born earlier than Mao Ze-dong”, and our QA system finally answered ‘‘Yes”. (2) The question ‘‘Whose subclasses include the Absolute and Precise Temporal Entity?” is an example of the second type of questions. (a) First, the question was converted into the formula Subclass (Absolute and Precise Temporal Entity, X), where X is a variable. (b) Then, our QA system called the agent ‘‘Absolute-and-Precise-Temporal-Entity-Agent”. This agent found Intersectionclass(Absolute and Precise Temporal Entity; Absolute Temporal Entity, Precise Temporal Entity) in its rule base, which means ‘‘Absolute and Precise Temporal Entity is an intersection of class of Absolute Temporal Entity and Precise Temporal Entity”. Further, this agent called the agents ‘‘Abstract-Temporal-Entity-Agent” and ‘‘Precise-Temporal-Entity-Agent”, and got Subclass(Abstract Temporal Entity, Temporal Entity) and Subclass(Precise Temporal Entity, Temporal Entity) in their respective rule bases. (c) Furthermore, the agent ‘‘Absolute-and-Precise-TemporalEntity-Agent” inferred Subclass(Absolute and Precise Temporal Entity, Temporal Entity) by applying theorem 1 in Section 3.2.3. This agent also deduced Subclass(Absolute and Precise Temporal Entity, Absolute Temporal Entity) and Subclass(Absolute and Precise Temporal Entity, Precise Temporal Entity) by employing definition 2 in Section 3.2.3. (d) Finally, our QA system outputted ‘‘Temporal Entity, Absolute Temporal Entity, and Precise Temporal Entity”. (3) We introduce the question ‘‘What is the temporal length of every Thursday in August 2010?” as an example of the third type of questions, and our QA system answered ‘‘96 h”. (a) First, the question was transformed into the formula ‘‘durationFn(every Thursday in August 2010, hour) = X”. (b) Then, the QA system called the agent ‘‘Category-of-LeftClosed-and-Right-Closed- Interval-Agent”, because ‘‘every Thursday in August 2010” is an instance of this class. This agent acquired the knowledge Contain(every Thursday in August 2010; August 5, August 12, August 19, August 26), which denotes that ‘‘every Thursday in August 2010 consists of four days: August 5, August 12, August 19, and August 26”. (c) Finally, this agent inferred that durationFn(every Thursday in August 2010, hour) = durationFn(August 5, hour) + durationFn (August 12, hour) + durationFn(August 19, hour) + durationFn (August 26, hour) = 96 by applying axiom (c) in Section 3.2.3 and the axiom 24 durationFn(T, day) = durationFn(T, hour) in Section 3.2.2. Therefore, our QA system answered ‘‘96 h”. (4) An example of the fourth type of questions is ‘‘Which solar year is the fifth lunar year of the Qian-long(乾隆 in Chinese) Reign?”.
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(a) First, our QA system converted the question into the formula nth-title-solar-yearFn(Title, 5, NULL, Qian-long, NULL) = X ”. (b) Then, the QA system called the agent ‘‘Lunar-Year-Agent”, since the fifth lunar year of the Qian-long Reign is an instance of the class of Lunar-Year. This agent found the knowledge starting-solar-yearFn(Title, NULL, Qian-long, NULL) = A.D.1736 in the knowledge base, which means that ‘‘The first lunar year of the Qian-long Reign is A.D.1736”. Here, NULL is a null value. (c) Finally, this agent derived nth-title-solar-yearFn(Title, 5, NULL, Qian-long, NULL) = A.D.1740 by employing the transformation axiom TCT1 in Section 3.3.2.3. Thus, our QA system answered ‘‘A.D.1740”. (5) The question ‘‘Which lunar year in the sixty year cycle is A. D.2010?” is an example of the fifth type of questions. (a) First, the question was transformed into the formula ‘‘stembranch-no(A.D.2010, lunar year, X)”. (b) Then, our QA system called the agent ‘‘Solar-Year-Agent”, because A.D.2010 is an instance of the class of Solar-Year. This agent inferred stem-branch-no(A.D.2010, lunar year, 27) by applying the transformation axiom TCT3 in Section 3.3.2.4, which shows that ‘‘the stem-branch combination representation of A.D.2010 is the 27th stem-branch combination”. (c) Finally, this agent got Index-stem-branch(Geng-yin, 27) according to Table 1 in Section 3.3.2.1, that is, ‘‘the 27th stem-branch combination is Geng-yin”. Hence, our QA system outputted ‘‘Geng-yin Lunar Year”. In summary, since DAML, OWL, KSL, KIF, Cyc, and our time ontologies all specify the topological temporal relations; they can answer the first type of questions. However, the taxonomy of classes of temporal entities with classification criterions, the properties of the intersection of class, and axioms of temporal entities are not constructed in DAML, OWL, KSL, KIF, and Cyc ontologies. These five ontologies are built based on the Gregorian calendar, and do not address the issues about time ontologies based on different calendars and the transformation between temporal entities in different timing systems. Therefore, the latter four types of questions could not be answered by these five ontologies. In addition, it is worth pointing out that our constructed Chinese time ontology can be applied to web services. In other words, it is capable of describing the temporal content of web pages and the temporal properties of web services. Here, we take the following example to illustrate this fact. To describe web services, we employ Ticket.com to demonstrate how our ontology supports OWL-S, which is a web service ontology based on the Web Ontology Language OWL [6,46]. Ticket.com is a fictitious ticket selling service site. A definition of an output parameter CollectTicketTime is shown in Fig. 7, and it specifies when users can collect tickets. CollectTicketTime has two properties EarliestCollectTicketTime and LatestCollectTicketTime that denote the earliest time and the latest time of collecting tickets for users, respectively. The ranges of these two properties are instances of the class Individual of Time Instant. The cardinalities for both properties are all one, which means that an instance of CollectTicketTime must have one and only one attribute value for each property. The values of EarliestCollectTicketTime and LatestCollectTicketTime are equal to PayTicketTime and MatchTime, that are times when users pay tickets and when matches begin, respectively.
5. Discussion We will explain how our development method of the Chinese time ontology could be used to build other time ontologies based on different calendars, and the reasons that our time ontology is significant and useful for other time ontoloiges construction.
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Fig. 7. A Definition of an output parameter CollectTicketTime.
Given any calendar c, e.g. the Hebrew calendar, the time ontology based on c can be constructed according to the following steps, as shown in Fig. 8. First, take our base time ontology as the base time ontology in the Hebrew time ontology. That is, the time system, the timing system, and the timing ontology within our base time ontology can be utilized as the model for time structure, temporal relations, the computation and representation of time, and classes of temporal entities and their relationships between these classes in the Hebrew time ontology. In this work setting, the Gregorian timing system can also be shared as the ‘‘time intermediator”. Then, develop the Hebrew timing system based on the Hebrew calendar according to the definition of the timing system, that is, time units, operations, functions, and axioms about the instants and intervals in the Hebrew calendar. Here, those axioms need to specify starting instants, ending instants, and duration lengths of calendar intervals. Finally, build the representing method for temporal entities in the Hebrew timing system, and the transformation method
The Time System Our Chinese Time Ontology
between temporal entities in the Hebrew timing system and entities in the Gregorian timing system. By following the methodology presented in this paper, this step will construct various representations of different kinds of temporal entities and their combined representations, and mapping relations between temporal entities in the Hebrew timing system and those in the Gregorian timing system. Thereby, the Hebrew ontology will have been built and can be used to represent and reason with temporal information described in Hebrew ways. The reasons that our time ontology is significant and useful for other time ontoloiges construction are given as follows. (1) The time system, the timing system, and the time ontology in the base time ontology can be employed independently or jointly as the foundation of other time ontologies for different purposes. (a) The time system gives two time primitives and all kinds of topological relations between time primitives with the least predicates, functions, and axioms, following the design criterion of ontology: minimal ontological commitment. So, the topological temporal relation between any two temporal entities can be represented by predicates, functions, and axioms in the time system. (b) The timing system provides a uniform model for various calendars and temporal expressions based on these calendars. It builds a formal model for starting times, ending times, and duration lengths of time units and their relationships. Thus, the timing system constitutes a bridge of transformation between any two temporal entities expressed based on different calendars. (c) The timing ontology builds temporal concepts and their attributes, relationships, and axioms, and the hierarchical taxonomy of temporal concepts with explicit criterions for concept classifications. The timing ontology is constructed following the seven-step method, which is the most mature method of building ontology [45]. Therefore, its respective parts can be selectively used for different temporal information applications. (2) In the process of building our time ontology, our approach meets the criteria of ontology development: clarity, extendibility, and minimal ontological commitment. Hence, our method can be reused to construct other time ontologies based on different calendars. (3) Within the issue about temporal representation and transformation, the divide and conquer technique is independent of any calendar and representative orders of different time units in different calendars. So it can be used to represent different granularities of temporal entities in other time ontologies and transform any two temporal entities in different time ontologies based on different calendars.
The Traditional Chinese Timing System
The Timing System The timing Ontology
The Gregorian Timing System
The Time System Hebrew Time Ontology
The Timing System The timing Ontology
The Hebrew Timing System
Axioms about the Traditional Chinese Calendar Intervals and Instants Representation of Temporal Entities based on the Traditional Chinese Calendar Axioms about the Gregorian Calendar Intervals and Instants Representation of Temporal Entities based on the Gregorian Calendar
Axioms about the Hebrew Calendar Intervals and Instants Representation of Temporal Entities based on the Hebrew Calendar
Fig. 8. An example of building other time ontologies.
Transformation
OWL definition of the OWL-S CollectTicketTime.owl 1 1
Transformation
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6. Conclusion In a nation with a long history, the time ontology is generally not purely based on the Gregorian calendar; therefore a more general conceptual model is necessitated in developing a time ontology for the Semantic Web and knowledge processing. In this paper, we introduced, in two steps, Chinese time ontology for the web services and knowledge systems involving temporal entities or properties. In the first step, we developed a base time ontology. The base time ontology includes a time system, a timing system, a timing ontology and a Gregorian timing system. The time system describes the time primitives, the time structure, and the topological relations between instants, intervals and events. The timing system provides a formal uniform model for a variety of specific timing systems. The timing ontology gives an explicit conceptual model for different kinds of temporal entities and their relations. In the second step, we introduced the other parts of the Chinese time ontology with the base time ontology as the basic and integral part: temporal measurement and representation in Chinese ways,
and transformation between temporal entities in the Gregorian and those in the traditional Chinese timing systems. As a result, our method of time ontology development could be used to build other time ontologies, and especially the base time ontology can be reused for other time ontologies. Acknowledgements The work is supported by two grants from the National Natural Science Foundation of China (#60705022 and #61035004) and a grant from the Ministry of Science and Technology (#2001CCA03000). The third author is also supported by the National 973 Project of China (#G1999032701) and the National Key Laboratory of Software Development Environment. Appendix A. Vocabulary of traditional Chinese calendar The table summarizes the vocabulary of traditional Chinese calendar, which is used in the paper.
Chinese Character Pronunciation
Explanation
Chinese Name
Chinese Character Pronunciation
Explanation
Chinese Name
Ai-xin-jue-luoMin-ning
An emperor’s name
Ri-zhong
A Shi-chen
日中
Bing Bu-shi Chen Chen-shi Chou Chou-shi
The 3rd celestial stem A Shi-chen The 5th terrestrial branch A Shi-chen The 2nd terrestrial branch A Shi-chen
爱新觉罗 旻宁 丙 哺时 辰 辰时 丑 丑时
Ren-ding San-geng Shen Shen-shi Shi-chen Shuo
人定 三更 申 申时 时辰 朔
Da-he Ding Ding-mao
An emperor’s reign title The 4th celestial stem A combination of Ding and Mao A Shi-chen A time unit
大和 丁 丁卯
Shi-shi Si Si-geng
A Shi-chen A Shi-chen The 9th terrestrial branch A Shi-chen A time unit The first lunar day of a lunar month A Shi-chen The 6th terrestrial branch A Shi-chen
二更 更
Si-shi Wang
庚 庚子
Er-geng Geng Geng Geng-zi Gui Gui-hai Hai Hai-shi Hua-jia Huang-hun Hui Ji-ming Ji Ji Jia Jia-zi Mao Mao Ze-dong Mao-shi Ping-dan Qian-long Qing Dynasty Ren Ri-die Ri-chu Ri-ru
The 7th celestial stem A combination of Geng and Zi The 10th celestial stem A combination of Gui and Hai The 12th terrestrial branch A Shi-chen A time unit A Shi-chen The last lunar day of a lunar month A Shi-chen The 6thcelestial stem A time unit A celestial stem A combination of Jia and Zi The 4th terrestrial branch The founder of modern China A Shi-chen A Shi-chen The reign title of an emperor A Chinese dynasty The 9th celestial stem A Shi-chen A Shi-chen A Shi-chen
食时 巳 四更 巳时 望
Wei Wei-shi
A Shi-chen The 15th lunar day of a lunar month The 8th terrestrial branch A Shi-chen
癸 癸亥
Wen-zong Wu
An emperor’s title The 5th terrestrial branch
文宗 午
亥 亥时 花甲 黄昏 晦
Wu Wu-shi Wu-geng Tang Dynasty Xin
The 7th celestial stem A Shi-chen A Shi-chen A Chinese dynasty The 8th celestial stem
戊 戊时 五更 唐朝 辛
鸡鸣 己 纪 甲 甲子
Xu Xu-shi Xuan-tong Xuan-zong Ye-ban
The 7th terrestrial branch A Shi-chen An emperor’s reign title An emperor’s title A Shi-chen
戌 戌时 宣统 宣宗 夜半
卯 毛泽东
Yi Yi-geng
The 2nd celestial stem A Shi-chen
乙 一更
卯时 平旦 乾隆
Yin Yin-shi You
The 3rd terrestrial branch A Shi-chen The 10th terrestrial branch
寅 寅时 酉
清朝 壬 日昳 日出 日入
You-shi Yu-zhong Zi Zi-shi
A Shi-chen A Shi-chen The 1st terrestrial branch A Shi-chen
酉时 隅中 子 子时
未 未时
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Contents lists available at ScienceDirect
Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys
A Chinese time ontology for the Semantic Web Chunxia Zhang a,⇑, Cungen Cao b, Yuefei Sui b, Xindong Wu c,d a
School of Software, Beijing Institute of Technology, Beijing 100081, China Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China c Department of Computer Science, University of Vermont, Burlington, VT 05405, USA d School of Computer Science and Information Technology, Hefei University of Technology, Hefei 230009, China b
a r t i c l e
i n f o
Article history: Received 23 December 2009 Received in revised form 29 April 2011 Accepted 29 April 2011 Available online 6 May 2011 Keywords: Time ontology Semantic Web Chinese time ontology Temporal entities Temporal representation
a b s t r a c t Representation of and reasoning with temporal knowledge are fundamental in information systems that involve changes and actions. To build such systems, a time ontology is demanded. The development of a time ontology is also an indispensable part of effort to realize the Semantic Web. Nevertheless, our practice shows that any practical time ontology is closely related with a specific calendar, culture or history. To this end, this paper presents a Chinese time ontology for knowledge systems and web services which involve temporal entities or temporal properties. First, we define a base time ontology. As a core component, it consists of a time system, a timing system, a Gregorian timing system, and a timing ontology. Upon this base ontology, other parts of the Chinese time ontology are finally constructed, including the traditional Chinese timing system, temporal representation in Chinese idiosyncratic ways, and transformation between temporal entities in the Gregorian timing system and temporal entities in the traditional Chinese timing system. We will argue that the base time ontology is not only a basic and integral part of the Chinese time ontology, but also a base for constructing other time ontologies. 2011 Elsevier B.V. All rights reserved.
1. Introduction One of the crucial problems in information and knowledge systems that involve action and change is the representation of and reasoning with time. To develop such systems, a time ontology is demanded. Building a time ontology is also necessary to realize the Semantic Web, which aims to provide automated web services based on the descriptions of the contents and capabilities of web resources [27,24]. A time ontology is a specification of a conceptualization for temporal knowledge. Currently, much effort has been made on building explicit time ontologies, such as the DAML ontology of time [17,18,42], the time ontology in OWL [47], KSL time ontology [44], the time ontology in KIF [48], Times and Dates in Cyc knowledge base [50], the time of DAML-S [43], the temporal portion of IEEE Standard Upper Ontology [49], and other works [11,15,28,32]. In working on time ontologies, our experience indicates that time ontologies are closely related with specific nations or cultures, though they may share a common part. This is especially true if nations, e.g. the Chinese nation, have a long history. For example, in our work on knowledge processing of Chinese historical knowledge [4], timing methods are associated with various historical events; in fact, each Chinese dynasty or kingdom had its ⇑ Corresponding author. E-mail addresses: [email protected] (C. Zhang), [email protected] (C. Cao), [email protected] (Y. Sui), [email protected] (X. Wu). 0950-7051/$ - see front matter 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.knosys.2011.04.021
own particular timing method. As another example, in our work on agricultural knowledge acquisition [5], we found that ancient farmers used a timing method of 24 Solar Terms for farming (e.g. what crops and animals are planted and raised during what solar terms?). Although no one exactly knows when this approach was created, it is still one of the dominant timing methods in Chinese societies. In spite of the great progresses in the past years, there are still two important issues about time ontologies that need to be further addressed, which constitute the motivation of this paper. One is that most existing ontologies count and express time according to the Gregorian calendar, and those ontologies are incapable of computing and representing time for people in societies with their own calendars. In other words, the effect of calendars in constructing time ontologies is simply ignored. However, calendars play an important role in building time ontologies. Actually, calendars are the basis of computing durations of and relationships between time units, and different calendars constitute different timing systems. In addition, to realize the Semantic Web, it is necessary for machines to be able to process and understand the semantics of temporal entities in various calendars on the World Wide Web [26]. Hence, it is indispensable to build up mappings between temporal entities in different timing systems within the same or different calendars. Another issue is the diversity of temporal computing and representation. Current time ontologies compute and express time mainly in a manner of the calendar date. However, there are other
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various approaches of computing and representing time that are related to a country’s culture, history, and agriculture and so on. People in different social-cultural contexts use different approaches to count and express time. This knowledge should also be addressed when building time ontologies. In this paper, we present a Chinese time ontology based on the current Chinese calendars: the Gregorian calendar and the traditional Chinese calendar. The Gregorian calendar is a kind of solar calendar, and is used almost everywhere in the world. The traditional Chinese calendar is a type of lunisolar calendar [39,51]. The ontology is developed for web services and knowledge systems that involve temporal entities or temporal properties. We build our ontology in two steps. First, we build a core component, called the base time ontology. Specifically, it consists of a time system, a timing system, a Gregorian timing system, and a timing ontology. Here, the Gregorian timing system is employed as a timing system based on the Gregorian calendar. Second, upon this base time ontology, we develop the other parts of the Chinese time ontology, including a traditional Chinese timing system, temporal representation in Chinese idiosyncratic ways, and transformation (mapping) between temporal entities in the Gregorian timing system and temporal entities in the traditional Chinese timing system. Here, the traditional Chinese timing system is a timing system founded on the traditional Chinese calendar. Furthermore, we will also argue that the base time ontology is not only a basic and integral part of the Chinese time ontology, but also a base for constructing other time ontologies. The remainder of this paper is organized as follows. Section 2 reviews the related work of time ontologies. Section 3 presents our Chinese time ontology. Section 4 compares our Chinese time ontology with other time ontologies, and introduces its applications in question answering and web services. The discussion is given in Section 5. Section 6 concludes this paper.
2. Related work Time is a basic attribute of data, information, and knowledge [7]. Temporal information processing has become a significant technique in the fields of information system, the Semantic Web, and natural language processing [25,33]. Time ontologies provide the measurement, computation and representation of time. Therefore, they are especially important for a variety of information systems such as electronic commerce, data warehouse, data mining, and decision support systems [10,13,20,21,33]. Temporal information has also penetrated into every aspect of the Internet; hence the specification of temporal information is necessary to realize the Semantic Web. Time ontologies are intended to give a specification of a conceptualization of temporal contents of web information and temporal properties of web services [25]. Natural language text is a main carrier of the web information. Time ontologies also play an important role in many natural language processing applications such as information retrieval, question answering, and text summarization [25,30]. It is difficult for applications involved in temporal knowledge to make significant progress without the explicit representation of the semantics of temporal information or properties. It is necessary to build a Chinese time ontology for processing temporal information which are represented in Chinese ways using any formal language or natural language. The DAML ontology of time [17,18,42] and the time ontology in OWL [47] use the first-order predicate calculus to represent temporal concepts and properties, including topological relations among instants, intervals, and events, measures of duration, the Gregorian calendar and clock terms, and times and durations. These two ontologies regard instants and intervals as temporal primitives. Times and Dates in Cyc knowledge base [50] aims to
build a temporal knowledge base of human commonsense knowledge. This knowledge base consists of assertions, rules, and commonsense ideas, which describe time points, properties of and relations between temporal objects, the calendar, and time of day and so on. The representation language of this knowledge base is the language CycL based on predicate calculus [50]. KSL time ontology treats time points and time intervals as temporal primitives on a time line [44]. This ontology is composed of the temporal class hierarchy structure, relations between time points and time intervals, time granularity and so on. The weaknesses of present time ontologies are given as follows. (1) The current ontologies are built based on the Gregorian calendar, so they can not compute and represent time expressed based on other calendars. Further, they neither consider the impacts of different calendars on time ontologies, nor build a conceptual model for various calendars. (2) They treat topological temporal relations, durations measure, times and durations description, and the calendar and clock, at a same conceptual level. In fact, the latter three parts are dependent on the Gregorian calendar. In our time ontology, those three parts are ingredients of the Gregorian timing system. (3) They neither give explicit classification criterions for temporal concepts, nor formal axioms for temporal concepts and their attributes. (4) Present ontologies compute and represent time in the form of the calendar date. However, they do not investigate the effect of a culture, history, and agriculture on temporal representations. The research tendency about time ontologies is the representation and transformation of deictic time (such as ‘‘last year”), aggregates of temporal entities (such as ‘‘every Monday”), and vague temporal entities (such as ‘‘recently”). A number of time theories have been proposed as formal bases for temporal knowledge representation and reasoning. Bruce [3], Kahn and Gorry [19], McCarthy and Hayes [22], McDermott [23], Shoham [31], and Halpern [16] all used the instant-based theory in their respective artificial intelligent systems. This theory was criticized for being unnatural or counterintuitive, and it also encountered the so-called Dividing Instant Problem [35]. Allen regarded the period as the ontological primitive of time [2], while Galton [12], Vila [34] treated both instants and intervals as time primitives. We choose instants and intervals as temporal primitives. Because the instant- and period-based time theory is more natural and intuitive, and can describe temporal knowledge more conveniently than a pure instant- or period-based time theory. It also satisfactorily addresses the problems that are confronted by the other two time theories, such as the Dividing Instant Problem and the expression of instantaneous events and instantaneous holding of the fluent [1,35]. Ontology can be classified into generic ontology, domain ontology, application ontology, and representation ontology. The research scope of this paper is to build a time ontology which is a kind of domain ontology. This paper focuses on two research questions: (1) how to build a base time ontology, which can be employed as a common core component of different time ontologies, and is irrelevant to any calendar, culture or language. (2) How to build a time ontology based on the traditional Chinese calendar and the Gregorian calendar. In this process, we have two assumptions about time primitives and time structure. One is that there are two time primitives: time instant and time interval, the other is that the time structure is linear and continuous. In contrast to the existing works, the main innovations of this paper are depicted as follows. (1) We propose the time system, the timing system, the timing ontology, and the Gregorian timing system to constitute the base time ontology. The former three components are independent of any calendar, language, or culture, while the last component acts as ‘‘a time intermediator”. (2) In order to process temporal information represented based on different calendars, this paper provides an approach for building the
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time ontologies based on different calendars. (3) Our time ontology builds a formal and explicit conceptualization of the temporal representation and transformation relating to the Gregorian calendar and the traditional Chinese calendar. In addition, we use a divide and conquer technique to represent temporal entity and transform temporal entities in different timing systems. Our time ontology provides various representation methods for different kinds of temporal entities in the traditional Chinese timing system, and constitutive methods of combined representations of these entities. Furthermore, temporal entities in the traditional Chinese timing system can be transformed into the corresponding temporal entities in the Gregorian timing system by using the converting formulas in this paper, and vise versa. The benefits and significances of this paper are given from the aspects of the base time ontology, the time ontology building method, and the temporal representation and transformation. (1) The time system, the timing system, and the timing ontology in the base time ontology are built in aspects of topology model, measure and representation model, and semantic model of time. Moreover, they are not affected by any calendar, culture, and representation language. From another point of view, conceptual models of time can be divided into a model involving measurement and a model not involving measurement. In this paper, the timing system and the timing ontology constitute the former model, while the time system is the latter model. The timing system is a conceptual model for various calendars, and the timing ontology is a conceptual model for temporal entities represented based on different calendars. Therefore, our base time ontology can be used into different levels of temporal representation and information applications across different calendars, cultures, and representation languages. (2) Our approach of building the Chinese time ontology complies with the criteria of ontology development: clarity, extendibility, and minimal ontological commitment [14]. (a) Clarity means that definitions of terms should be objective, complete, and be stated in logical axioms, where a complete definition of a term means that it is defined by necessary and sufficient conditions [14]. For example, each class of temporal entities in the timing ontology is specified with formal and complete definitional axioms. (b) An ontology with the minimal ontology commitment should specify the minimal constraints about the objects being modeled [14]. As an illustration, in the Gregorian timing system and the traditional Chinese timing system, starting times, ending times, and temporal lengths of the three basic time units (including year, month, and day) are given in formal axioms, and starting times, ending times, and temporal lengths of other time units can be defined based on those axioms. (c) An ontology with extendibility should provide a conceptual basis, and new terms can be defined based on present terms without the revision of the present ontology [14]. For instance, for the temporal representation in the traditional Chinese timing system, any new representation method and its transformation method of lunar year, lunar month, lunar day, and hour can be easily added to the present ontology; and any new combined representation of temporal entities can also be added. Hence, our ontology building method makes our ontology and can make other time ontologies built by that method with more flexibility, portability, and extendibility. (3) For the temporal representation and transformation, a divide and conquer technique is employed to express temporal entity and transform temporal entities in different tim-
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ing systems. For a temporal entity te in the traditional Chinese timing system, it can be divided into one or multiple temporal entities te11, te12, . . . , te1k, each of which involve only a time unit, according to representing methods of lunar years, lunar months, lunar days, and hours. Here, te1i (i = 1, 2, . . . , k) includes one or multiple representing methods of a time unit. Thereby, we build constitutive methods of combined representation of different kinds of temporal entities. In addition, te11, te12, . . . , te1k can be transformed into temporal entity te21, te22, . . . , te2k in the Gregorian timing system according to the transforming formulas in this paper, respectively. Further, te21, te22, . . . , te2k are integrated to constitute a temporal entity in the Gregorian timing system, which is the corresponding temporal entity of te. Thus, this kind of technique makes it easier to express various granularities of temporal entities in the traditional Chinese timing system and to transform between them and temporal entities in the Gregorian timing system. 3. A Chinese time ontology We will present the framework of our Chinese time ontology, the contents of the base time ontology and other parts of the Chinese time ontology in this section. 3.1. The framework of the Chinese time ontology The framework of the Chinese time ontology is illustrated in Fig. 1. The base time ontology is composed of a time system, a timing system, and a timing ontology, which are built on topological level, measure and representation level, and semantic level of time, respectively. The time system gives the time primitives, the time structure, and the topological relations between instants, intervals, and events. The timing system is a formal and general conceptual model for various methods of computing and representing time. For temporal entities expressed by any kind of timing system in any formal or natural language, the timing ontology includes classes of temporal entities, attributes of classes, relationships between classes, and semantic axioms constraining the interpretation and application of these terms. Therefore, the time system, the timing system, and the timing ontology are independent of any calendar, culture, and language. The Gregorian timing system and the traditional Chinese timing system are two instances of the timing system. The Gregorian timing system consists of axioms about instants and intervals in the Gregorian calendar, and the representation of temporal entities based on this calendar. This system is included in the base time ontology. The traditional Chinese timing system contains axioms about instants and intervals in the traditional Chinese calendar and the representation of temporal entities founded on this calendar. Other parts of our Chinese time ontology comprise the traditional Chinese timing system and the transformation between temporal entities in the Gregorian timing system and those in the traditional Chinese timing system. In the following, we use the first-order predicate calculus as the representation language of our time ontology, which has been employed to represent various domain-specific ontologies including mathematics, archaeology, geography, and history and so on in our former works [5,36]. It is noted that the time ontology has nothing to do with any ontology representation language. 3.2. The base time ontology We assume a linear and continuous time structure for the Chinese time ontology. That is, the time line is isomorphic to the set of real numbers and is unbounded.
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Part 1:The Base Time Ontology
Our Chinese Time Ontology
The Time System Topological Level The Timing System Measure and Representation Level
The Gregorian Timing System
Axioms about the Gregorian Calendar Intervals and Instants Representation of Temporal Entities based on the Gregorian Calendar
The timing Ontology Semantic Level Transformation between Temporal Entities
IS-A Relation Part-Whole Relation Transformation Relation
The Traditional Chinese Timing System
Axioms about the Traditional Chinese Calendar Intervals and Instants Representation of Temporal Entities based on the Traditional Chinese Calendar
Part 2: Other Parts of Our Chinese Time Ontology Fig. 1. The framework of our Chinese time ontology.
3.2.1. The time system As argued previously, we consider the time system to have two time primitives: time instant (or instant for short) and time interval (or interval for short). The time system is intended to give topological temporal relations between instants themselves, between intervals themselves, and between instants and intervals, and relations between events and time [37]. Let the type of the time instants be r and the type of the time intervals be s. A time system contains (1) Three predicates instant(t), interval(T) and temporal-entity(x) to denote that t is an instant, T is an interval and x is a temporal entity, respectively. (2) Two functions startFn(x) and endFn(x): s ? r. (3) Two predicates before(t1, t2): r r ? X, inside(t, T): r s ? X, where X is the type of Boolean values {true, false}. By the types of functions and predicates, we have the following formal axioms. (1) Instants and intervals are disjoint; that is, a temporal entity is either an instant or an interval, as shown in axiom (c) below. (a) "t (instant(t) ? temporal-entity(t)) (b) "T (interval(T) ? temporal-entity(T)) (c) "x (temporal-entity(x) ? (instant(x) ^ : interval(x)) _ (:instant (x) ^ interval(x))) (2) before(t1, t2) means that t1 is before t2, which gives directionality to time. The before relation is irreflexive, asymmetric, transitive and linear, as shown in the following axioms (a)–(d): (a) "t1 (:before(t1, t1)) (b) "t1 "t2 (before(t1, t2) ? :before(t2, t1)) (c) "t1 "t2 "t3 (before(t1, t2) ^ before(t2, t3) ? before(t1, t3)) (d) "t1 "t2 (before(t1, t2)_before(t2, t1)_(t1 = t2)) (3) startFn(T) and endFn (T) represent the starting and ending instants of T, respectively. Axioms (c) and (d) below say that there exist unique starting and ending instants for each interval. The starting instant of T is always before its ending one, shown in axiom (e). (a) "T "t ((startFn(T) = t) ? interval(T) ^ instant(t)) (b) "T "t ((endFn (T) = t) ? interval(T) ^ instant(t))
(c) "T "t1 "t2 ((startFn(T) = t1) ^ (startFn(T) = t2) ? t1 = t2) (d) "T "t1 "t2 ((endFn (T) = t1) ^ (endFn (T) = t2) ? t1 = t2) (e) "T "t1"t2 ((startFn(T) = t1) ^ (endFn (T) = t2) ? before(t1, t2)) (4) The predicate inside(t, T) expresses a relation between an instant and an interval, meaning that t is an instant within T. The following axiom means that every interval is closed in the sense that it contains its starting and ending instants.
8t 8tTðinsideðt; TÞ $ ðt ¼ startFnðTÞÞ _ ðt ¼ endFnðTÞÞ _ ðbeforeðstartFnðTÞ; tÞ ^ beforeðt; endFnðTÞÞÞÞ (5) Relations between intervals are given by the following axioms, which are based on the before relations between their beginning and ending instants. (a) precedes(T1, T2) means the ending instant of T1 is before the starting instant of T2.
precedesðT 1 ; T 2 Þ $ beforeðendFnðT 1 Þ; startFnðT 2 ÞÞ (b) meets(T1, T2) means the ending instant of T1 is the same as the starting instant of T2.
meetsðT 1 ; T 2 Þ $ endFnðT 1 Þ ¼ startFnðT 2 Þ (c) overlaps(T1, T2) signifies that the starting instant of T1 is before that of T2, the starting instant of T2 is before the ending instant of T1, and the ending instant of T1 is before that of T2. Formally,
overlapsðT 1 ; T 2 Þ $ beforeðstartFnðT 2 Þ; endFnðT 1 ÞÞ ^ beforeðstartFnðT 1 Þ; startFnðT 2 ÞÞ ^ beforeðendFnðT 1 Þ; endFnðT 2 ÞÞ (d) starts(T1, T2) means that the starting instant of T1 is same as that of T2, and the ending instant of T1 is before that of T2. Formally,
startsðT 1 ; T 2 Þ $ ðstartFnðT 1 Þ ¼ startFnðT 2 ÞÞ ^ beforeðendFnðT 1 Þ; endFnðT 2 ÞÞ (e) during(T1, T2) means that the starting instant of T1 is after that of T2, and the ending instant of T1 is before that of T2. Formally,
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duringðT 1 ; T2 Þ $ beforeðstartFnðT 2 Þ; startFnðT 1 ÞÞ ^ beforeðendFnðT1 Þ; endFnðT2 ÞÞ (f) finishes(T1, T2) means that the starting instant of T1 is before that of T2, and the ending instant of T1 is same as that of T2. Formally,
finishesðT 1 ; T 2 Þ $ ðendFnðT1 Þ ¼ endFnðT2 ÞÞ ^ beforeðstartFnðT1 Þ; startFnðT 2 ÞÞ (g) equals(T1,T2) denotes that the starting instant of T1 is the same as that of T2, and the ending instant of T1 is the same as that of T2. Formally,
equalsðT 1 ; T 2 Þ $ ðstartFnðT 1 Þ ¼ startFnðT 2 ÞÞ ^ ðendFnðT 1 Þ ¼ endFnðT 2 ÞÞ (6) We will give axioms about relating an event with an instant or interval. First, at-instant(e, t) means that an event e occurs at an instant t. Now, we define four predicates for events occurring during intervals. The predicate cc-during(e, T) shows e occurs continuously during an interval T, including its starting and ending instants1. We also use other three relevant predicates: oo-during(e, T), oc-during(e, T) and co-during(e, T), depending on whether e occurs at the starting and ending instants of T. For example, co-during(e, T) means that e occurs at every instant of T, including its starting instant but excluding its ending instant. (a) "e "T (cc-during(e, T) M "t (inside(t, T) ? at-instant(e, t))) (b) "e"T (oc-during(e, T) M "t (inside(t, T) ^ t – startFn(T) ? at-instant(e, t))) (c) "e"T (co-during(e, T) M "t (inside(t, T) ^ t – endFn(T) ? at-instant(e, t))) (d) "e"T (oo-during (e, T) M "t (inside (t, T) ^ t – startFn(T) ^t – endFn(T) ? at-instant(e, t)))
3.2.2. The timing system and the Gregorian timing system A timing system S consists of the following ingredients: (1) A language L; (2) Axioms about calendar intervals and instants; (3) Temporal entities and terms expressing those entities. A language L for S is a triple (U, O, F), where (1) a set U of units for time instants and intervals; (2) a set O of operations. We assume that first and last are two built-in operations such that given a string r of symbols, first(r) is the first symbol of r, last(r) is the last symbol of r. (3) a set F of functions. durationFn(T, u) is the amount of time within an interval T as measured in a unit u. For instance, U in the Gregorian timing system is given below.
U ¼ fðcenturyÞ; ðdecadeÞ; ðyearÞ; ðmonthÞ; ðweekÞ; ðdayÞ; ðhourÞ; ðminuteÞ; ðsecondÞg: As an example, a string r = ‘‘2008(year)08(month)08(day)20 (hour)08(minute)00(second)” is a term in this timing system, simply denoted by ‘‘2008:08:08:20:08:00” in the international standard time notation2, and first(r) = (year), last(r) = (second). 1 Note that cc- means that the left-closure and right-closure of T are counted in; that is, the event also occurs at both the starting and ending instants of T. This explanation is applicable to oc-, co- and oo-, where o means the event does not occur at the corresponding instant. 2 http://www.cl.cam.ac.uk/~mgk25/iso-time.html.
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In the following we will give axioms about calendar intervals and instants in the Gregorian timing system. We use the predicate solar-year(x) to show that x is an instance of the class Solar Year, month(x, m) to denote that x is an instance of the class of the mth Month, and the function successorFn(x, u) to be the successor of x in a time unit u. For example, if y = successorFn(1, month), then month(y, 2) holds. Here, t4 is an instant of 0:00 on the solar day when the sun returns to the Vernal Equinox, t5 is an instant of 24:00 on the solar day before the solar day on which the sun returns to the Vernal Equinox next time, and ‘‘” is the logical operator exclusive or. (a) solar-year(x) ? (startFn(x) = t4) ^ (endFn(x) = t5) ^ ((durationFn (x, day) = 365) (durationFn(x, day) = 366)) (b) month(x, 1) ? "y(solar-year(y) ^ contains(y, x) ? startFn(x) = startFn(y)) (c) month(x, 12) ? "y(solar-year(y) ^ contains(y, x) ? endFn(x) = endFn(y)) (d) month (x, m) ^ (y = successorFn(x, month)) ? "z(solar-year(z) ^ contains(z, x) ^ contains(z, y) ? endFn(x) = startFn(y)) (e) month (x, 1) _ month (x, 3) _ month(x, 5) _ month(x, 7) _ month (x, 8) _ month(x, 10) _ month(x, 12) ? durationFn(x, day) = 31 (f) month(x, 2) ? (durationFn(x,day) = 28) (durationFn(x, day) = 29) (g) month(x, 4) _ month(x, 6) _ month(x, 9) _ month(x, 11) ? durationFn(x, day) = 30 Predicates decade(x) and century(x) say that x is an instance of the class of Decade and Century, respectively. Axioms about decades and centuries are given as follows. Here, t6 and t8 are instants of 0:00 on the first solar day of the solar year which can be divided exactly by 10 and 100, respectively; t7 is an instant of 24:00 on the last solar day of the solar year that is the sum of the starting solar year of the decade and 9; t9 is an instant of 24:00 on the last solar day of the solar year that is the sum of the starting solar year of the decade and 99. (a) decade(x) ? (startFn(x) = t6) ^ (endFn(x) = t7) ^ (durationFn(x, year) = 10) (b) century(x) ? (startFn(x) = t8) ^ (endFn(x) = t9) ^ (durationFn(x, year) = 100) For example, axioms below reflect relations between some time units. (a) 60 durationFn(T, hour) = durationFn (T, minute) (b) 24 durationFn (T, day) = durationFn (T, hour) (c) 12 durationFn (T, year) = durationFn (T, month) What time an instant is in is relative to the time zone. For example, if the local time was 9:00 on January 2, 2010 in Beijing located in the 8th Eastern Time Zone, then the local time was 21:00 on January 1, 2010 in Washington located in the 5th Western Time Zone. Predicate time-of(t; y, m, d, h, n, s; z) is defined for this, where y, m, d, h, n and s are integers, 1 6 m 6 12, 1 6 d 6 31, 0 6 h 6 24, 0 6 n 6 60, 0 6 s 6 60, and z is a world time zone. Axiom (a) below states the relations between times in different time zones. Axiom (b) shows a method of computing the duration of an interval T whose starting and ending instants are in different time zones. Here, durationof(T, Dy, Dm, Dd, Dh, Dn, Ds) denotes that the duration of T is Dy years, Dm months, Dd days, Dh hours, Dn minutes, and Ds seconds, and the values of these six arguments are real numbers. (a) time-of(t; y, m, d, h, n, s; GMT) M time-of(t; y, m, d, h x, n, s; the xth western time zone) ^ time-of(t; y, m, d, h + x, n, s; the xth eastern time zone) ^ (1 6 x 6 12)
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(b) "T "t1 "t2 ((startFn(T) = t1) ^ (endFn (T) = t2) ^ time-of(t1; y1, m1, d1, h1, n1, s1; z) ^ time-of(t2; y2, m2, d2, h2, n2, s2; z) ? durationof(T; y1 y2, m1 m2, d1 d2, h1 h2, n1 n2, s1 s2)) 3.2.3. The timing ontology This subsection will introduce the components of the timing ontology: classes of temporal entities, attributes of classes, and relationships between classes, and formal semantic axioms. We first give some basic definitions. Definition 1. Given a class C1 and its instance I1, the property space of I1 is the set of all properties that I1 satisfies, written as proins(I1); the property space of C1 is the set of common properties of all instances of C1, written as procla(C1). For example, procla(Precise Temporal Entity) is a set of common properties of all instances of the class of Precise Temporal Entity, where these instances (e.g. from A.D.2000 to A.D.2010) have the unique starting and ending instants. Definition 2. Given two classes C1 and C2, if procla(C1) procla(C2), we say that C2 is a subclass of C1, and C1 is a super-class of C2. Definition 3. Given a class C and its subclasses SC1, SC2, . . . , SCn, an instance I of C, if the following formula holds, then we say that the classification {SC1, SC2, . . . , SCn} of C is a partition of C, where i, j and n are natural numbers, 1 6 i, j 6 n.
8i8j ðði–jÞ ! :9IðproinsðIÞ proclaðSC i Þ [ proclaðSC j ÞÞÞ ^ð
n \
proclaðSC i Þ ¼ proclaðCÞÞ
i¼1
() :9IðproinsðIÞ ðproclaðSC 1i Þ [ proclaðSC 2p ÞÞ [ ðproclaðSC 1j Þ [ proclaðSC 2q ÞÞÞ () :9IðproinsðIÞ ððproclaðSC 1i Þ [ proclaðSC 1j ÞÞ [ ðproclaðSC 2p Þ [ proclaðSC 2q ÞÞÞÞ Since {SC11, SC12, . . . , SC1n} and {SC21, SC22, . . . , SC2m} are two partitions of C1, then the following two formulas hold based on the definition of the partition.
8i8jðði–jÞ ! :9IðproinsðIÞ proclaðSC 1i Þ [ proclaðSC 1j ÞÞÞ 8p8qððp–qÞ ! :9IðproinsðIÞ proclaðSC 2p Þ [ proclaðSC 2q ÞÞÞ: Hence, we get the formula below.
8i8j8p8qðði – jÞ ^ ðp – qÞ ! :9IðproinsðIÞ ðproclaðSC 1i Þ [ proclaðSC 1j ÞÞ [ ðproclaðSC 2p Þ [ proclaðSC 2q ÞÞÞÞ That is, 8i8j8p8qððip – jqÞ ! :9IðproinsðIÞ proclaðCC ip Þ[ proclaðCC jq ÞÞÞ: (4) Because {SC11, SC12, . . . , SC1n} and {SC21, SC22, . . . , SC2m} are T two partitions of C1, then we obtain ni¼1 proclaðSC 1i Þ ¼ proclaðC 1 Þ Tm and j¼1 proclaðSC 2j Þ ¼ proclaðC 1 Þ. Furthermore,
proclaðCC 11 Þ \ \ proclaðCC 1m Þ \ \ proclaðCC n1 Þ \ \ proclaðCC nm Þ () ðproclaðSC 11 Þ [ proclaðSC 21 ÞÞ \ \ ðproclaðSC 11 Þ [ proclaðSC 2m ÞÞ \ \ ðproclaðSC 1n Þ [ proclaðSC 21 ÞÞ \ \ ðproclaðSC 1n Þ [ proclaðSC 2m ÞÞ () ðproclaðSC 11 Þ [ ðproclaðSC 21 Þ \ \ proclaðSC 2m ÞÞÞ \ ðproclaðSC 12 Þ [ ðproclaðSC 21 Þ \ \ proclaðSC 2m ÞÞÞ \ \ ðproclaðSC 1n Þ
Definition 4. Given a class C1 and its subclasses SC1, SC2, and a class C2, if the following formula holds, then we say that C2 is an intersection of class of SC1 and SC2.
proclaðSC 1 Þ [ proclaðSC 2 Þ ¼ proclaðC 2 Þ According to definitions of the subclass and the intersection of class, we can deduce Theorem 1 below. Based on the definitions of the partition and the intersection of class, we can infer Theorem 2. Theorem 1. Given a class C1 and its subclasses SC1 and SC2, if C2 is an intersection of class of SC1 and SC2, then C2 is a subclass of C1. Proof. If C2 is an intersection of class of SC1 and SC2, then procla S (SC1) procla(SC2) # procla(C2) holds based on the definition of the intersection of class. Since SC1 and SC2 are subclasses of C1, then procla (C1) procla(SC1) and procla(C1) procla(SC2) hold according to the definition of the subclass. Further, we have procla(C1) procla(C2), that is, C2 is a subclass of C1. h Theorem 2. Given two partitions {SC11, SC12, . . . , SC1n} and {SC21, SC22, . . . , SC2m} of C1, if 8i8jðproclaðCC ij Þ ¼ proclaðSC 1i Þ [ procla ðSC 2j ÞÞ, then {CC11, CC12, . . . , CC1m, CC21, . . . , CC2m, . . . , CCn1, . . . , CCnm} is a partition of C1, that is, the set of all intersection of classes of these two partitions is a partition of C1. Proof. (1) Based on Theorem 1, we get that CC11, . . . , CC1m, CC21, . . . , CC2m, . . . , CCn1, . . . , CCnm are subclasses of C1. (2) For any two intersection of classes CCip and CCjq (1 6 i, j 6 n, 1 6 p, q 6 m), we have
:9IðproinsðIÞ proclaðCC ip Þ [ proclaðCC jq ÞÞ
[ ðproclaðSC 21 Þ \ \ proclaðSC 2m ÞÞÞ () ðproclaðSC 11 Þ \ proclaðSC 12 Þ \ \ proclaðSC 1n ÞÞ [ ðproclaðSC 21 Þ \ proclaðSC 22 Þ \ \ proclaðSC 2m ÞÞ () proclaðC 1 Þ [ proclaðC 1 Þ () proclaðC 1 Þ According to the definition of the partition, we can infer that {CC11, CC12, . . . , CC1m, CC21, . . . , CC2m, . . . , CCn1, . . . , CCnm} is a partition of C1. h In this paper, the taxonomy of classes of temporal entities and formal models for these classes are an extension of our previous work [38]. In the work [38], there are four classifications of the class of Temporal Entity (TE): Time TE and Duration, Precise TE and Fuzzy TE, Absolute TE and Relative TE, and Direct TE and Indirect TE. In addition, formal models of TE and these eight subclasses have been constructed in the work [38]. In this paper, we further build a classification of Time TE (shown in Fig. 2) and formal models for eleven subclasses of Time TE. It is pointed out that every classification of each class in this taxonomy is a partition of this class. Time TE is divided into Individual of TE such as ‘‘September.21.2009” and Category of TE such as ‘‘autumn every year” based on whether it denotes a collection of temporal entities with certain common properties. Individual of TE is partitioned into Individual of Time Instant and Individual of Time Interval according to its topological structure. Further, Individual of Time Interval includes Individual of Left Open and Right Open Interval, Individual of Left Closed and Right Open Interval, Individual of Left Open and Right Closed Interval, and Individual of Left Closed and Right Closed Interval in terms of continuity of intervals. For example, ‘‘From 2000 to 2009” is an instance of the last class. Category of TE is segmented into Category of Time Instant and Category of Time Interval based on its topological structure. Category of Time Interval only comprises a subclass of Category of Left Closed and
C. Zhang et al. / Knowledge-Based Systems 24 (2011) 1057–1074
Time Temporal Entity Individual of Temporal Entity Individual of Time Instant Individual of Time Interval Individual of Left Open and Right Open Interval Individual of Left Closed and Right Open Interval Individual of Left Open and Right Closed Interval Individual of Left Closed and Right Closed Interval Category of Temporal Entity Category of Time Instant Category of Time Interval Category of Left Closed and Right Closed Interval hyponymy Relationship Fig. 2. The taxonomy of time temporal entity.
Right Closed Interval (e.g. from January to March every year) grounded on continuity of intervals. As illustration, we will give the model for the class of Category of Left Closed and Right Closed Interval. This class possesses four attributes: value, modifier, number of the set of discontinuous intervals, and duration length. The set of discontinuous intervals means that any two intervals T1 and T2 in this set satisfy precedes(T1, T2) or precedes(T2, T1). Axioms are classified into four types based on objects they describe: axioms of memberships of classes, properties of attributes, relationships between attributes, and relationships between classes [38]. Examples of each type of axioms are given below: (a) category-of-lcrc-interval(T) M $k((T = T1 [ T2 [ [Tk) ^ (k > 1) ^ "i((1 6 i 6 k) ^ individual-of-lcrc-interval(Ti)) ^ "i((1 6 i < k) ^ before(endFn(Ti), startFn(Ti+1)))) (b) category-of-lcrc-interval(T) ? (number-of-disc-intervalFn(T) > 1) (c) category-of-lcrc-interval(T) ^ $k((k = number-of-disc-intervalFn (T)) ^ (T = T1[ [Tk) ^ "i((1 6 i 6 k) ^ individual-of-lcrc-interval(Ti))) ? "u(durationFn(T, u) = durationFn(T1, u) + . . . + durationFn(Tk, u)) (d) time-temporal-entity(x) M (individual-of-temporal-entity(x) ^ : category-of-temporal- entity(x)) _ (:individual-of-temporal-entity (x) ^ category-of-temporal-entity(x)) Axiom (a) means that T is an instance of Category of Left Closed and Right Closed Interval if and only if T is composed of at least two discontinuous intervals which are instances of Individual of Left Closed and Right Closed Interval. Axiom (b) says that the number of discontinuous intervals of T is greater than one. Axiom (c) expresses that the duration length of T is equal to the sum of duration lengths of discontinuous intervals included in T. Axiom (d) represents relations between Time TE and its two subclasses: Individual of TE and Category of TE. Here, function number-of-disc-intervalFn(T) is the number of discontinuous intervals included in T, predicate time-temporal-entity(x) denote that T is an instance of Time TE, and predicates individual-of-temporal-entity(x), individual-of-lcrc-interval(T), category-of-temporal-entity(x), and category-of-lcrc-interval(T) have the analogous meanings.
3.3. Other parts of the Chinese time ontology With the construction of the base time ontology, another task in developing the Chinese time ontology is to build formal models for temporal measurement and representation in Chinese ways, and transformation methods between temporal entities in the Gregorian timing system and those in the traditional Chinese timing system. First we need to mention one point: whether a temporal
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entity is an instant or interval is generally a pragmatic question. For example, we could consider the date ‘‘January 1, 2010” as an instant, and say that an event occurs on that day; or we could consider the date as an interval, and say that an event occurs during that day. 3.3.1. The traditional Chinese timing system We first introduce 24 Solar Terms, which are the basis of setting lunar years and lunar months, and the unique timing method in the world. The 24 Solar Terms divide the ecliptic into 24 equal segments, with 15 of the Sun’s longitude between two terms. Solar terms of even degrees are called major solar terms. The 24 Solar Terms reflect seasonal alternations, weather changes, agricultural activities, etc., and play a significant role in ordinary life and activities. In the traditional Chinese timing system, the set of time units is {(Hua-jia(花甲 in Chinese)), (Ji(纪 in Chinese)), (Lunar Year), (Lunar Month), (Lunar Day), (Shi-chen(时辰 in Chinese)), (Geng (更 in Chinese))} (see Appendix for Chinese terms and their explanations). As a calendar interval, a time unit u has its specific starting instant, ending instant and duration length L. In contrast, when it acts as a duration, it is any interval whose duration length is L. (a) A Hua-jia is a cycle of sixty consecutive lunar years. It starts from the Jia-zi(甲子 in Chinese) lunar year, and ends in the Gui-hai (癸亥 in Chinese) lunar year. (b) A Ji is only used as an instance of Duration, and is any interval whose duration length is 12 lunar years, not as an instance of Time TE. (c) A lunar year is a period of time having 12 lunar months. (d) A lunar month is a period of 29 or 30 days. (e) A lunar day is a period of time having 24 h. A day in the traditional Chinese calendar is different from one in the Gregorian calendar in starting and ending instants, as shown in axiom (a) and (b) below. For distinguishing days in two calendars, we use a lunar day for a day in the traditional Chinese calendar. (f) A Shi-chen or a Geng is a period of time having 2 h. We introduce predicates common-lunar-year(x) and leap-lunaryear(x) to denote x is an instance of the class of Common Lunar Year, and Leap Lunar Year, respectively. Predicates lunar-month(x), lunarday(x), hua-jia(x), ji(x), shi-chen(x), and geng(x) have the analogous meanings. We use t10 for a starting instant on the new moon lunar day, t11 for an ending instant on the lunar day before the next new moon lunar day, t12 for a starting instant on the first lunar day of the lunar month which contains the solar term Spring Showers, t13 for an ending instant on the lunar day before the first lunar day of the lunar month which contains the next Spring Showers, t14 for a starting instant on the first lunar day of the Jia-zi lunar year, and t15 for an ending instant on the last lunar day of the Gui-hai lunar year. (a) solar-day(x) ? (startFn(x) = 0:00 on the day x) ^ (endFn(x) = 24:00 on the day x) ^ (durationFn(x, hour) = 24) (b) "x "y "T(lunar-day(x) ^ solar-day(y) ^ (startFn(x) = startFn (T)) ^ (startFn(y) = endFn(T)) ^ (durationFn(T, hour) = 1) ? (startFn(x) = 23:00 on the solar day before the solar day y) ^ (endFn (x) = 23:00 on the solar day y) ^ (durationFn(x, hour) = 24)) (c) lunar-month(x) ? ((startFn(x) = t10) ^ (endFn (x) = t11)) ^ ((durationFn(x, lunar day) = 29) (durationFn(x, lunar day) = 30)) (d) common-lunar-year(x) ? ((startFn(x) = t12) ^ (endFn (x) = t13)) ^ (durationFn(x, lunar month) = 12) (e) leap-lunar-year(x) ? durationFn(x, lunar month) = 13 (f) hua-jia(x) ? (startFn(x) = t14) ^ (endFn (x) = t15) ^ (durationFn (x, lunar year) = 60) (g) ji(x) ? durationFn(x, lunar year) = 12 W (h) shi-chen(x) geng(x) ? durationFn(x, hour) = 2
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3.3.2. Representation and transformation of lunar years This subsection will introduce three representing systems for lunar years and transformation between lunar years and solar years. These systems are: the Stem-Branch System, the Animal Sign System, and the Emperor’s Title and Reign Title System. 3.3.2.1. The Stem-Branch System for lunar years representation. The Stem-Branch System has been used as a principal timing method since ancient times [40]. The system is composed of the ten sequential celestial stems (Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui) and the twelve sequential terrestrial branches (Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai) as shown in Table 1. The system is a totally ordered set of the 60 ordered combinations of celestial stems and terrestrial branches (called stembranch combinations). Table 1 lists those 60 ordered combinations, and the number indicates the index of each combination. For example, the first combination is Jia-zi, which consists of the first celestial stem Jia and the first terrestrial branch Zi. The second combination is Yi-chou, which consists of the second celestial stem Yi and the second terrestrial branch Chou. Those sixty stem-branch combinations express a cycle of 60 lunar years. For instance, A.D.1924, A.D.1984, A.D.2044 and so on are called the Jia-zi Lunar Year, and are instances of the class of Jia-zi Lunar Year, while A.D.1925, A.D. 1985, A.D.2045 and so on are called the Yi-chou Lunar Year. The period from A.D.1924 to A. D.1983 is a complete cycle, so is from A.D.1984 to A.D.2043. Note that, due to the circularity of the sixty stem-branch combinations, each combination actually denotes a class of lunar years. 3.3.2.2. The Animal Sign System for lunar years representation. The 12 Animal Sign System is a totally ordered set of the 12 ordered animal signs, and is used to represent a cycle of 12 lunar years. The first and second rows in Table 2 show the 12 animal signs and their orders. Each animal sign corresponds to a fixed terrestrial branch (shown in Table 2), and denotes a class of lunar years with an identical terrestrial branch. For example, A.D.1984, A.D.1996 and A.D.2008 are called the Rat Lunar Year, and are instances of
the class of Rat Lunar Year, and they all correspond to the first terrestrial branch (Zi). 3.3.2.3. The emperor’s title and reign title system for lunar years representation. In Chinese history, most emperors used their titles or reign titles to express lunar years. Each emperor in a dynasty started counting lunar years by his or her first year of reign as the first lunar year of using the emperor’s title or reign titles. For instance, the title of emperor Ai-xin-jue-luo Min-ning(爱新觉罗旻 宁 in Chinese) in the Qing Dynasty (清朝 in Chinese) is Xuan-zong (宣宗 in Chinese) during his rule from A.D.1821 to A.D.1850, so A. D.1821 is called the first lunar year of the Emperor Xuan-zong Aixin-jue-luo Min-ning of the Qing Dynasty. Let Sd is the set of all dynasties, Sep is the set of all emperors, Sty be the set of {Title, Reign Title}, Set is the set of titles or reign titles of all emperors, Sy is the set of solar years, and N is the set of natural numbers. We introduce three functions below. These functions are to obtain the starting solar year, the ending solar year, and the nth solar year of the title or reign title et of the emperor ep in the dynasty d, and ty denotes the type of et. We have the axiom TCT1. (a) starting-solar-yearFn(ty, ep, et, d): Sty Sep Set Sd ? Sy. (b) ending-solar-yearFn(ty, ep, et, d): Sty Sep Set Sd ? Sy. (c) nth-title-solar-yearFn(ty, n, ep, et, d): Sty N Sep Set Sd ? S y. TCT1. (starting-solar-yearFn(ty, ep, et, d) = sy1) ^ ^ (ending-solaryearFn(ty, ep, et, d) = sy2) ? (nth-title-solar-yearFn(ty, n, ep, et, d) = sy1 + n 1) ^ (1 6 n 6 sy2 sy1 + 1) For emperor Ai-xin-jue-luo Min-ning of the Qing Dynasty, we have the following facts. (a) starting-solar-yearFn(Title, Ai-xin-jue-luo Min-ning, Xuanzong, Qing) = A.D.1821. (b) ending-solar-yearFn(Title, Ai-xin-jue-luo Min-ning, Xuanzong, Qing) = A.D.1850.
Table 1 The 60 ordered combinations of celestial stems and terrestrial branches in the stem-branch system.
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Animal sign Terrestrial branch
1
2
3
4
5
6
7
8
9
10
11
12
Rat Zi
Ox Chou
Tiger Yin
Rabbit Mao
Dragon Chen
Snake Si
Horse Wu
Sheep Wei
Monkey Shen
Rooster You
Dog Xu
Pig Hai
(c) nth-title-solar-yearFn(Title, n, Ai-xin-jue-luo Min-ning, Xuanzong, Qing) = A.D.(1821 + n 1), where 1 6 n 6 30.
3.3.2.4. Transformation between lunar years and solar years. In the following, we discuss transformation methods between solar years and lunar years. First, we introduce some functions and predicates. (1) In order to use our Chinese time ontology practically, an instant t is required to be identifiable. For example, (a) if t refers to a solar/lunar month, then the solar/lunar year which the month belongs to is specified in t; (b) if t refers to a solar/lunar day, then both the solar/lunar year and month which the day belongs to is also specified in t. Based on this, we introduce functions yearFn(t, sl1), monthFn(t, sl1), dayFn(t, sl1), hourFn(t, sl2), and shi-chenFn(t, sl3), where sl1 e {solar, lunar}, sl2 e {solar}, and sl3 e {lunar}. The ranges of these five functions are the sets of all representations of the solar/lunar year, month, day, hour, and Shi-chen which t belongs to, respectively. (2) last-lunar-dayFn(ly, lm) is a function which gets the index of the last lunar day of the lunar month lm in the lunar year ly. Here, ly and lm are representations for lunar years and lunar months, respectively. (3) The function modFn(x, n) calculates the remainder of an integer x divided by a positive integer n, and 0 6 modFn(x, n) < n. (4) Let v belongs to the set {lunar year, lunar month, lunar day, Shi-chen}, the predicate stem-branch-no(t, v, n) means that the stem-branch combination representation of v to which t belongs is the nth index of the Stem-Branch System. Accordingly, we define predicates celestial-stem-no(t, v, n) and terrestrial-branch-no(t, v, n). (5) Predicate stem-branch-combination(sb, s, b) is true when the sth celestial stem and the bth terrestrial branch constitute the sbth stem-branch combination. As shown in Table 1, not all combinations of celestial stems and terrestrial branches are meaningful in the Stem-Branch System. In fact, they must satisfy TCT2 below. TCT2. "sb"s"b(stem-branch-combination(sb, s, b) M (s = 10 modFn(10 sb, 10) ^ b = 12 modFn(12 sb, 12))) For a given temporal entity in the Gregorian timing system, we often need to calculate its corresponding temporal entity in the traditional Chinese timing system and vice versa. First, we consider mapping relationships between solar years and lunar years. This calculation is given in TCT3, TCT4, TCT5 and TCT6 below, where k is an integer. TCT7 is used to calculate the celestial stem and the terrestrial branch representations for a solar year. TCT3. "t "y(before(A.D.1, t) ^ y = yearFn(t, solar) ? stem-branch-no(t, lunar year, 60-modFn(3-modFn(y, 60), 60))) TCT4, "t "y(before(t, B.C.1) ^ y = yearFn(t, solar) ? stem-branch-no(t, lunar year, 60- modFn(modFn(y, 60) + 2, 60))) TCT5. "t "x(before(A.D.1, t) ^ stem-branch-no(t, lunar year, x)
? yearFn(t, solar) = 60k + x 57) TCT6. "t"x(before(t, B.C.1) ^ stem-branch-no(t, lunar year, x) ? yearFn(t, solar) = 60k x + 58) TCT7. "t "m(stem-branch-no(t, lunar year, m) ? celestial-stem-no (t, lunar year, 10-modFn(10-m, 10)) ^ terrestrial-branch-no(t, lunar year, 12-modFn(12-m, 12))) As illustration, we calculate the stem-branch combination representation of the solar year A.D.2008 as follows. (a) Since before(A.D.1, A.D.2008) is true and 60 modFn (3 modFn(2008, 60), 60) = 25, stem-branch-no(A.D.2008, lunar year, 25) is true according to TCT3. (b) The 25th stem-branch combination is Wu-zi by referring to Table 1, so we say that A.D.2008 is an instance of the class of Wu-zi Lunar Year. 3.3.3. Representation and transformation of lunar months There are two commonly used methods of expressing lunar months. The first method is based on ordinal numbers, i.e. the first lunar month, . . . , the twelfth lunar month. The second method is based on the Stem-Branch System. The celestial stem of any lunar month of any lunar year can be specified by the celestial stem of this lunar year, and the inference formula is shown in TCT8. For example, if the celestial stem of a lunar year is Jia or Ji, then the celestial stem of the first lunar month in this lunar year is Bing. If the celestial stem of a lunar year that t belongs to is unknown, the celestial stem of a lunar month which t belongs to can be inferred by the solar year that t belongs to, as shown in TCT9. TCT10 and TCT11 are formulas to transform between the terrestrial branch representation of a lunar month and its ordinal number representation. TCT8. "t "lm "n(lm = monthFn(t, lunar) ^ celestial-stem-no(t, lunar year, n) ?celestial-stem-no(t, lunar month, modFn(2 modFn(n, 5) + lm, 10))) TCT9. "t"lm(lm = monthFn(t, lunar) ^ (y = yearFn(t, solar)) ?celestial-stem-no(t, lunar month, modFn(lm + 2 modFn(y, 5) 6, 10))) TCT10. "t "lm(lm = monthFn(t, lunar) ?terrestrial-branch-no(t, lunar month, modFn(lm + 2, 12))) TCT11. "t "x "y(terrestrial-branch-no(t, lunar month, x) ? (y = monthFn(t, lunar)) ^ (y = x + 12k 2) ^ (1 6 y 6 12)) 3.3.4. Representation and transformation of lunar days The four main ways for representing lunar days are the approaches based on ordinal numbers, the Stem-Branch System, the phases of the moon, and the traditional Chinese festivals. The Stem-Branch System for lunar days’ denotation uses the 60 stembranch combinations to express lunar days. This counting method has so far the longest history among the day counting methods in the world. During each lunar month, the moon has several special phases, which are used to represent lunar days. These phases include Shuo (朔 in Chinese, i.e. new moon), Wang (望 in Chinese, i.e. full moon) and Hui(晦 in Chinese, i.e. the last lunar day of a lunar month). For each instant t which involves a phase of the Moon,
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we use the function moon-phaseFn(t) to means the moon phase in which t is. Then we have the following facts about moon phases. (a) (moon-phaseFn(t) = Shuo) M (dayFn(t, lunar) = 1) (b) (moon-phaseFn(t) = Wang) M (dayFn(t, lunar) = 15) (c) (ly = yearFn(t,lunar)) ^ (lm = monthFn(t, lunar)) ^ (moon-phaseFn(t) = Hui) M (dayFn(t, lunar) = last-lunar-dayFn(ly, lm)) The main traditional Chinese festivals have the Spring Festival or the Chinese New Year, the Lantern Festival, the Dragon Boats Festival, the Middle Autumn Festival, the Double Ninth Festival, and the Chinese New Year’s Eve. Function Chinese-festivalFn(t) is used to denote the Chinese festival which t is in. For example, W (Chinese-festivalFn(t) = Spring Festival) (Chinese-festivalFn(t) = Chinese New Year) M (monthFn(t, lunar)=1) ^ (dayFn(t, lunar) = 1) 3.3.5. Representation and transformation of hours There exist three methods of expressing hours of a lunar day: the approaches based on colors of the sky, the terrestrial branch, and the clapper, as shown in Fig. 3. Chinese ancient people averagely divided a lunar day into twelve segments, and each segment is called a Shi-chen. The 12 Shi-chen are named Ye-ban(夜半 in Chinese), Ji-ming(鸡鸣), Ping-dan(平旦), Ri-chu(日出), Shi-shi(食时), Yuzhong(隅中), Ri-zhong(日中), Ri-die(日昳), Bu-shi(晡时), Ri-ru(日入), Huang-hun(黄昏), and Ren-ding(人定), as shown in Fig. 3. These names have meanings relating to the natural law of sunrise and sunset, changes of the sky color, and people’s living customs. For instance, Ji-ming means the time when roosters call, that is, the period from 1:00 am to 3:00 am. As illustration, we give an axiom about Ji-ming, where the function shi-chenFn(t) represents the Shichen that t is in, and SC is the set of 12 Shi-chen. (a) (sc = shi-chenFn(t) ^ sc = Ji-ming) M (startFn(sc) = 1:00 am) ^ (endFn(sc) = 3:00 am) (b) "sc((sc SC) ^ durationFn(sc, hour) = 2) The terrestrial branch is also used to denote Shi-chen. Each Shichen corresponds to a fixed terrestrial branch. For instance, Ji-ming is also called Chou-shi, whose terrestrial branch is Chou. The 12 Shi-chen are sequentially named Zi-shi, Chou-shi, Yin-shi, Mao-shi, Chen-shi, Si-shi, Wu-shi, Wei-shi, Shen-shi, You-shi, Xu-shi, and Hai-shi, as shown in Fig. 3. As an example, an axiom about Ji-ming is (shi-chenFn(t) = Ji-ming) M terrestrial-branch-no(t, shi-chen, 2). Hours can also be represented by the Stem-Branch System. The celestial stem of a Shi-chen is specified by the celestial stem of the lunar day in which the Shi-chen is, as shown in TCT12.
TCT12. "m"n(terrestrial-branch-no(t, shi-chen, m) ^ celestialstem-no(t, lunar day, n) ?celestial-stem-no(t, shi-chen, modFn(2 modFn(n, 5) 1, 10) + modFn(m 1, 10))) For example, let t is in the Shi-chen of Chou-shi on September 21, 2008, the steps of computing the stem-branch combination representation of this Shi-chen are as follows: (a) The stem-branch combination representation of September 21, 2008 is Jia-zi, so celestial-stem-no(September 21, 2008, lunar day, 1) is true. (b) Since t is in the Shi-chen of Chou-shi, terrestrial-branch-no(t, shi-chen, 2) holds. (c) Based on TCT12, we have celestial-stem-no(t, shi-chen, modFn (2 modFn(n, 5) 1, 10) + modFn(m 1,10)) = celestial-stemno(t, shi-chen, modFn(2 modFn(1, 5) -1, 10) + modFn(21,10)) = celestial-stem-no(t, shi-chen, 2). (d) Because the second celestial stem is Yi, the stem-branch combination denotation of the Chou-shi on September 21, 2008 is the Shi-chen of Yi-chou. The approach based on the clapper for hours counting segments an interval from 7:00 pm to 5:00 am on the next lunar day into five consecutive sub-intervals: Yi-geng(the first Geng), Er-geng(the second Geng), San-geng(the third Geng), Si-geng(the fourth Geng) and Wu-geng(the fifth Geng), as shown in Fig. 3. For instance, we give an axiom about Yi-geng, where the function gengFn(t) shows the Geng that t is in.
ðg ¼ gengFnðtÞ ^ g ¼ Yi-gengÞ $ ðstartFnðgÞ ¼ 7 : 00 pmÞ ^ ðendFnðgÞ ¼ 9 : 00 pmÞ As seen from the 12 Shi-chen, Yi-geng, Er-geng, San-geng, Sigeng and Wu-geng correspond to Wu-shi, Hai-shi, Zi-shi, Choushi and Yin-shi, respectively. For example,
8g 8scððg ¼ Yi gengÞ ^ ðsc ¼ Wu shiÞ ! equalðg; scÞÞ 3.3.6. Combined representations of temporal entities In spoken and written Chinese, many temporal expressions use more than one method for representing a temporal entity, and are called combined ones. For example, the lunar year of Jia-zi and Rat utilizes two representing methods of lunar years: the Stem-Branch System and the Animal Sign System. This subsection will discuss various combined representations for different periods of time: lunar years, lunar months, lunar days and hours. Based on the three representing methods of lunar years, there are ten types of combined representations of lunar years, as shown
Fig. 3. The approach based on colors of the sky, the terrestrial branch, and the clapper for hours representation.
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C. Zhang et al. / Knowledge-Based Systems 24 (2011) 1057–1074 Table 3 Ten types of combined representations of lunar years. No.
The title of a reigning dynasty
1 2 3 4 5 6 7 8 9 10
p
p p p
Emperor’s title
p p p p
Emperor’s name
Emperor’s reign title p p p p
p p
The ordinal number p p
The stembranch
The terrestrial branch
The Animal Sign
p
p p p
p p p p p p
in Table 3. The first row of Table 3 gives the components of combined representations of lunar years: (1) the title of a reigning dynasty, (2) the emperor’s title, (3) the emperor’s name, (4) the emperor’s reign title, (5) the ordinal number of a lunar year, (6) the stem-branch combination representation for a lunar year, (7) the terrestrial branch representation for a lunar year, (8) the animal sign representation for a lunar year. Information in Table 3 will p be filled using ‘ ’ to indicate that it is a component in a certain kind of combined representations. An example of the seventh type of combined representations is the ninth lunar year of the Da-he reign of Emperor Wen-zong of the Tang Dynasty(唐朝文宗大和九年 in Chinese). It includes (a) the title of a reigning dynasty: the Tang Dynasty; (b) the emperor’s title: Wen-zong; (c) the emperor’s reign title: Da-he; (d) the ordinal number of the lunar year: the ninth lunar year. And its corresponding solar year is A.D.835. Combined representations of lunar months are composed of one of ten kinds of combined representations of lunar years above and one of two kinds of representations of lunar months. For instance, the fourth lunar month of the third lunar year of the Xuan-tong reign (宣统三年四月 in Chinese), whose corresponding solar month is May 1911, contains (a) the emperor’s reign title, i.e., Xuan-tong; (b) the ordinal number of the lunar year, i.e., the third lunar year; (c) the ordinal number of the lunar month, i.e., the fourth lunar month. For combined representations of lunar days, they consist of a combined representation of a lunar year above, and one of eight types of combined representations of a lunar month and a lunar day, as shown in Table 4. As illustration, the full moon day of the third lunar month of the Ding-mao lunar year(丁卯年三月望日 in Chinese) is an example of the third type of combined representations. And it comprises: (a) the stem-branch combination of the lunar year: Ding-mao; (b) the ordinal number of the lunar month: the third lunar month; (c) the moon phase of the day: the full moon day. And its corresponding solar day is April 12, 1987 and other dates. A combined representation of a Shi-chen is composed of a combined representation of a lunar year, a combined representation of a lunar month and a lunar day, and one of three kinds of representa-
tions of Shi-chen. For instance, the Ren-ding Shi-chen of the Geng-zi day of the second lunar month of the second lunar year of the Xuantong reign (宣统二年二月庚子日人定时 in Chinese) means the period from 9:00pm to 11:00 pm on April 5, 1910. It includes (a) the emperor’s reign title: Xuan-tong; (b) the ordinal number of the lunar year: the second lunar year; (c) the ordinal number of the lunar month: the second lunar month; (d) the stem-branch combination of the day: Geng-zi; (e) the color of the sky of the Shi-chen: Ren-ding. 3.3.7. Completeness of transformation approaches With the discussion of transformation between solar years/ months/days/hours and lunar years/months/days/Shi-chen, we must consider a problem: are there formulas to make a conversion between any temporal entity in the Gregorian timing system and any temporal entity in the traditional Chinese timing system? Fig. 4 illustrates transforming relationships between temporal entities expressed by different representing methods. The left part of Fig. 4 shows temporal entities of different periods in the traditional Chinese timing system, while the right part of Fig. 4 gives temporal entities of different periods in the Gregorian timing system. Arrows ‘M’, ‘?’, , and indicate that there is a one-toone mapping, an injective mapping, a surjective mapping and a one-to-many relationship of transformation between two sets of temporal entities on the two ends of arrows, respectively. As illustration, there is a one-to-one mapping of transforming relation between the set of Shi-chen represented by the terrestrial branch system and the set of hours expressed by the ordinal numbers according to formulas in Section 3.3.5. For another example, if S1 and S2 are the sets of lunar days denoted by approaches based on the moon phrases and the ordinal numbers, respectively, then there exists an injective mapping of the converting relation from S1 to S2, in terms of formulas in Section 3.3.4. For the third example, there is a one-to-many transforming relation from the set S3 of lunar years described by the Stem-Branch system to the set S4 of solar years denoted by the ordinal numbers, while there is a surjective mapping of the converting relation from S4 to S3. We can make
Table 4 Eight types of combined representations of lunar days. No.
1 2 3 4 5 6 7 8
Lunar years
Lunar months
One of the 10 kinds of combined representations of lunar years p p p p p p p p
The ordinal number p p p
Lunar days The stembranch
The ordinal number p
The phase of the moon
The traditional Chinese festival
p p p p p
p
The stembranch
p p p
p p p p
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A one-to-one mapping An injective mapping A surjective mapping A one-to-many relation
Lunar Years Represented by the Animals Zodiac System
Temporal Entities in the traditional Chinese Timing System
Lunar Years Represented by the Emperor’s and Reign Title System
Lunar Months Represented by the Stem-Branch System Lunar Days Lunar Days Represented Represented by the Approach by the Approach based on based on Phases Traditional of the Moon Chinese Festivals
Shi-chen Represented by the Approach based on Colors of the Sky
Temporal Entities in the Gregorian Timing system
Lunar Years Represented by the Stem-Branch System
Lunar Months Represented by the Approach based on Ordinal Numbers Lunar Days Represented by the Stem -Branch System
Shi-chen Represented by the Approach based on the Clapper
Solar Years Represented by the Approach based on Ordinal Numbers
Solar Months Represented by the Approach based on Ordinal Numbers
Lunar Days Represented by the Approach based on Ordinal Numbers
Shi-chen Represented by the Terrestrial Branch System
Solar Days Represented by the Approach based on Ordinal Numbers
Hours Represented by the Approach based on Ordinal Numbers
Fig. 4. Transformation relationships between temporal entities expressed by different representing methods.
transformation between solar years and lunar years depicted by the Stem-Branch System in the light of formulas in Section 3.3.2.4. It is noticed that there is neither the accurate formula to make a conversion between a solar month and a lunar month, nor the algorithm to do a transformation between a solar day and a lunar day. Because the mutation and rotation of the moon and the sun are uneven, unstable, and wobbling, the length of a solar month is not always greater than the length of a lunar month, and a lunar month might contain two major solar terms. Two points should be emphasized here. First, the New Year’s Day in the Gregorian calendar does not always coincide with the Chinese New Year’s day (i.e. the Chinese Spring Festival’s day), so the mapping between a solar year and a lunar year is only approximate. For example, the New Year’s Day of 2008 in the Gregorian calendar is January 1, while the Chinese New Year started on February 7, 2008. More precisely, for the period from January 1, 2008 to February 6, 2008, the lunar year that it belongs to is an instance of the class of Ding-hai Lunar Year. However, the lunar year including the period from February 7, 2008 to December 31, 2008 is an instance of the class of Wu-zi Lunar Year. Furthermore, the animal sign of a person, who was born during the first period, is Pig. However, the animal sign of a person who was born during the second period is Rat. The second point is that the Stem-Branch System for lunar years representation was used from the Western Han Dynasty; so later people calculated the stem-branch combination representations of lunar years before that time. 4. Comparison and application of our Chinese time ontology 4.1. Comparison with other time ontologies We use the CommonKADS evaluation framework to compare our Chinese time ontology with current main time ontologies, since the framework is the leading methodology to support structured knowledge engineering [6,29,41]. These ontologies include the DAML ontology of time [18], time ontology in OWL [47], KSL time ontology [44], time ontology in KIF [48], and times and dates in Cyc knowledge base [50].
The DAML Ontology of Time Topological Temporal Relations
Our Chinese Time Ontology
The time System
The Timing System
The Timing Ontology
Measuring Durations The Gregorian Calendar and Clock Describing Times and Durations The IS-A Relation
The Gregorian Timing System
The Traditional Chinese Timing System
Transformation between Temporal Entities The Part-Whole Relation
The Corresponding Relation between Two Time Ontologies
Fig. 5. Comparison of the DAML ontology of time and our Chinese time ontology.
Fig. 5 illustrates the comparison and the corresponding relationships between components of the DAML ontology of time and ones of our Chinese time ontology. The DAML ontology consists of four components: topological temporal relations, measuring durations, the Gregorian calendar and clock, and describing times and durations. Our ontology comprises the time system, the timing system, the timing ontology, the Gregorian timing system, the traditional Chinese timing system, the transformation between temporal entities in the Gregorian timing system and those in the traditional Chinese timing system. The first component in the DAML ontology corresponds to the time system in our base time ontology, and they all depict topological temporal relations between time primitives, and linking time and events. The contents of the other three components are included in the Gregorian timing system within our base time ontology. Tables 5–7 show the comparison between our base time ontology with DAML, OWL, KSL, KIF and Cyc time ontologies in aspects of components, domain knowledge, and concepts and taxonomies. Information in these three tables will be filled using ‘+’ to indicate that it is a supported feature in the time ontology, ‘’ for non supported features. In Table 5, all six time ontologies define topological temporal relations, the Gregorian calendar and clock, and times
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Topological temporal relations Durations measure The Gregorian calendar and clock Times and durations description The timing system The timing ontology
The DAML ontology of time
Time ontology in OWL
KSL time ontology
Time ontology in KIF
Times and dates in Cyc
Our base time ontology
+ + + +
+ + + +
+ + + +
+ + + +
+ + +
+ + + + + +
Table 6 Comparison of main components of domain knowledge in six time ontologies.
Concepts Hyponymy relations Functions Instances Axioms Axioms of membership of concepts Axioms of properties of attributes Axioms of relations between attributes Axioms of relations between concepts
The DAML ontology of time
Time ontology in OWL
KSL time ontology
Time ontology in KIF
Times and dates in Cyc
Our base time ontology
+ + + +
+ + + +
+ + + +
+ +
+ + + +
+ + + +
+ + + +
Table 7 Comparison of concepts and taxonomies in six time ontologies.
Components including temporal concepts Notations for sets of temporal concepts Cardinalities of sets of temporal concepts Relations between sets
Disjoint decompositions Subclass partitions Criterions for concept classification
The DAML ontology of Time
Time ontology in OWL
KSL time ontology
Time ontology in KIF
Times and dates in Cyc
Our base time ontology
Topological temporal relations Sd
Topological temporal relations Sw
KSL time ontology Sk
Times and dates in Cyc Sc
The time system Ss
The Timing Ontology So
3
5
14
7
3
23
Sw Sd
|Sk \ Sd| = 2 |Sk \ Sw| = 2
|Sc \ Sd| = 2 |Sc \ Sw| = 2 |Sc \ Sk| = 2
Ss = Sd
+ +
+
+
+
+ + +
|So \ Sd| = 3 |So \ Sw| = 3 |So \ Sk| = 6 |So \ Sc| = 2 + + +
and durations description. Duration measure is included in four time ontologies excepting KSL and Cyc. The timing system and the timing ontology are only built in our base time ontology. Table 6 indicates the main components of domain knowledge: concepts (i.e. classes of temporal entities), hyponymy relations, functions, instances, and axioms. All six time ontologies support definitions of functions and instances, while five ontologies other than KIF give concepts and their hyponymous relations. It is mentioned that axioms about concepts and attributes are only specified in our base time ontology, and these axioms are given in Section 3.2.3. Fig. 6 gives temporal concepts and their taxonomies in the DAML, OWL, KSL, and Cyc time ontologies. Table 7 summarizes the most important features to be analyzed when describing concepts and taxonomies in an ontology: cardinalities of sets of temporal concepts, relations between these sets, disjoint decompositions, subclass partitions, and criterions for concept classification. The feature of disjoint decompositions means that (a) there may be an instance I1 of a concept C, I1 is not an instance of any sub-concepts of C for a classification; (b) there does not exist an instance I2 of C, I2 is an instance of more than one sub-concept of C for a classification. This feature is supported by five ontologies excepting KIF. Taxonomies in the DAML and our base time ontologies satisfy the property of subclass partitions. Only our base time ontology provides explicit criterions for every classification of each concept.
In brief, the comparison measurement among our base time ontology, DAML, OWL, KSL, KIF, and Cyc time ontologies focuses on components and domain knowledge. The comparison measurement of domain knowledge includes eight features: concepts, hyponymy relations, functions, instances, and axioms about membership of concepts, properties of attributes, relations between attributes, and relations between concepts. Further, the comparison about concepts and taxonomies consists of five features: cardinalities of sets of temporal concepts, relations between these sets, disjoint decompositions, subclass partitions, and criterions for concept classification. In conclusion, the main differences between present time ontologies and our time ontology are given as follows based on the above comparison. (a) The key difference is that we propose the time system, the timing system and the timing ontology to compose the base time ontology. (b) Formal axioms are an indispensable component in our timing ontology. However, other ontologies do not provide formal semantic axioms for temporal entities and their properties. Axioms can be used for constraining the interpretation and use of temporal concepts and their relationships. (c) In contrast with the representation of temporal entities in the Gregorian timing system, there are a variety of representing methods for different kinds of temporal entities in the traditional Chinese timing system. We analyzed these approaches, and built
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The DAML Ontology of Time Temporal Entity Instant Interval
Temporal Entity Time Ontology in OWL Instant Interval Proper Interval Date Time Interval
Time Granularity Time interval Time Point
Temporal Thing Convex Time Interval Temporal Quantity Calendar Month Temporal Stuff Type Non-Convex Time Interval Time Interval Regular Non-Convex Time Interval Temporal Object Type Calendar Day Temporally Disjoint Temporal Object Type Left Open Interval Time Instant Right Open Interval Time Interval Open Right Open Interval Right Close Interval Time Interval Closed Times and Dates in Cyc
KSL Time Ontology
Fig. 6. Temporal concepts and their taxonomies in four time ontologies.
constitutive methods of combined representations of temporal entities. In particular, we have constructed the formulas in the first-order predicate calculus for transformation between temporal entities in the Gregorian and the traditional Chinese timing systems. We aim to provide a method for developing models of temporal measurement, representation, and transformation based on different calendars. 4.2. Applications of our chinese time ontology This subsection will illustrate an application of time ontologies to question answering. We will show which types of questions could be answered by our Chinese time ontology but could not be completed by DAML [18], OWL [47], KSL [44], KIF [48], and Cyc time ontologies [50]. This application is built up on our developed question answering system (QA system) with a Chinese encyclopedic knowledge base [5,8,9,36]. This knowledge base covers twenty-one domains such as medicine, biology, history, geography, mathematics, and archaeology. It comprises more than 3,000,000 assertions, and more than one thousand temporal attributes such as Geological Age of the concept Archaeological Site and Manufacturing Time of the concept Ancient Firearm. Our QA system consists of four major components: a natural language user interface, an encyclopedic knowledge base, domain-specific multi-agent systems for answering and reasoning about users’ questions, and a multi-agent communication protocol [5,8,9]. Each agent represents a class of entities, includes axioms, theorems, and properties rules about this class of entities as its rule base for making inferences, and shares the encyclopedic knowledge base. When our QA system receives a question from a user,
it will take the following main steps to generate the answer. First, it transforms a question in a natural language into a formula represented in the first-order predicate calculus. Second, it calls the agents which represent the classes of entities, and judge whether these classes or their instances are involved in the question. Third, these called agents search the encyclopedic knowledge base and their rule bases, and perform forward or backward reasoning until inferring the answer or completing the searching process. In experiments, we give five types of questions to illustrate the capability of our Chinese time ontology and other time ontologies in question answering. Specially, these questions cover five issues about topological temporal relations, the taxonomy of classes of temporal entities, axioms of temporal entities, the representation of temporal entities, and the transformation between temporal entities in different timing systems. Table 8 lists the types of the questions, examples of those questions, and their answers. As can be seen from Table 8, only the first type of questions could be completed by DAML, OWL, KSL, KIF, and Cyc time ontologies, while all types of questions could be answered by using our Chinese time ontology. The details of how our Chinese time ontology is employed to answer these questions are described as follows. (1) An example of the first type of questions is ‘‘Whether was Karl Heinrich Marx born earlier than Mao Ze-dong(毛泽东 in Chinese)?”, and our QA system answered ‘‘Yes”. There are three steps for answering this question. (a) Our QA system transformed this question into the formula ? Birth-time-earlier-than(Karl Heinrich Marx, Mao Ze-dong), where ‘‘?” means the question is a general question.
Table 8 Examples of types of questions and answers. No.
Types of questions
Questions
Answered by DAML, OWL, KSL, KIF, or Cyc Ontologies
Answers
1
Topological Temporal Relations
Yes
Yes
2
Taxonomy of Classes of Temporal Entities
No
3
Axioms of Temporal Entities
No
Temporal Entity, Absolute Temporal Entity, Precise Temporal Entity 96 hours
4
Representation of Temporal Entities
No
A.D.1740
5
Transformation between Temporal Entities in Different Timing Systems
Whether was Karl Heinrich Marx born earlier than Mao Ze-dong? Whose subclasses include the Absolute and Precise Temporal Entity? What is the temporal length of every Thursday in August 2010? Which solar year is the fifth lunar year of the Qian-long Reign? Which lunar year in the sixty year cycle is A.D.2010?
No
Geng-yin Lunar Year
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(b) Then, the QA system called the agent ‘‘Person-Agent”, since Karl Heinrich Marx and Mao Ze-dong are instances of the class of Person. This agent searched the knowledge about birth times of Mao Ze-dong and Karl Heinrich Marx, and obtained the assertions ‘‘Mao Ze-dong was born in A. D.1893”, ‘‘Karl Heinrich Marx was born earlier than Vladimir Ilich Lenin”, and ‘‘Vladimir Ilich Lenin was born in A.D.1870”. They are represented as Birth-time(Mao Ze-dong, A.D.1893), Birth-time-earlier-than(Karl Heinrich Marx, Vladimir Ilich Lenin), and Birth-time(Vladimir Ilich Lenin, A.D.1870) in the knowledge base, respectively. Further, this agent deduced Birth-time-earlier-than(Vladimir Ilich Lenin, Mao Ze-dong). (c) The agent ‘‘Person-Agent” got the assertion that the relation ‘‘Birth-time-earlier-than” is an instance of the before relation in its rule base. And this agent inferred that this relation satisfies the transitiveness, because it inherits the transitiveness of the before relation in the time system. Hence, this agent derived Birth-time-earlier-than(Karl Heinrich Marx, Mao Ze-dong), i.e. ‘‘Karl Heinrich Marx was born earlier than Mao Ze-dong”, and our QA system finally answered ‘‘Yes”. (2) The question ‘‘Whose subclasses include the Absolute and Precise Temporal Entity?” is an example of the second type of questions. (a) First, the question was converted into the formula Subclass (Absolute and Precise Temporal Entity, X), where X is a variable. (b) Then, our QA system called the agent ‘‘Absolute-and-Precise-Temporal-Entity-Agent”. This agent found Intersectionclass(Absolute and Precise Temporal Entity; Absolute Temporal Entity, Precise Temporal Entity) in its rule base, which means ‘‘Absolute and Precise Temporal Entity is an intersection of class of Absolute Temporal Entity and Precise Temporal Entity”. Further, this agent called the agents ‘‘Abstract-Temporal-Entity-Agent” and ‘‘Precise-Temporal-Entity-Agent”, and got Subclass(Abstract Temporal Entity, Temporal Entity) and Subclass(Precise Temporal Entity, Temporal Entity) in their respective rule bases. (c) Furthermore, the agent ‘‘Absolute-and-Precise-TemporalEntity-Agent” inferred Subclass(Absolute and Precise Temporal Entity, Temporal Entity) by applying theorem 1 in Section 3.2.3. This agent also deduced Subclass(Absolute and Precise Temporal Entity, Absolute Temporal Entity) and Subclass(Absolute and Precise Temporal Entity, Precise Temporal Entity) by employing definition 2 in Section 3.2.3. (d) Finally, our QA system outputted ‘‘Temporal Entity, Absolute Temporal Entity, and Precise Temporal Entity”. (3) We introduce the question ‘‘What is the temporal length of every Thursday in August 2010?” as an example of the third type of questions, and our QA system answered ‘‘96 h”. (a) First, the question was transformed into the formula ‘‘durationFn(every Thursday in August 2010, hour) = X”. (b) Then, the QA system called the agent ‘‘Category-of-LeftClosed-and-Right-Closed- Interval-Agent”, because ‘‘every Thursday in August 2010” is an instance of this class. This agent acquired the knowledge Contain(every Thursday in August 2010; August 5, August 12, August 19, August 26), which denotes that ‘‘every Thursday in August 2010 consists of four days: August 5, August 12, August 19, and August 26”. (c) Finally, this agent inferred that durationFn(every Thursday in August 2010, hour) = durationFn(August 5, hour) + durationFn (August 12, hour) + durationFn(August 19, hour) + durationFn (August 26, hour) = 96 by applying axiom (c) in Section 3.2.3 and the axiom 24 durationFn(T, day) = durationFn(T, hour) in Section 3.2.2. Therefore, our QA system answered ‘‘96 h”. (4) An example of the fourth type of questions is ‘‘Which solar year is the fifth lunar year of the Qian-long(乾隆 in Chinese) Reign?”.
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(a) First, our QA system converted the question into the formula nth-title-solar-yearFn(Title, 5, NULL, Qian-long, NULL) = X ”. (b) Then, the QA system called the agent ‘‘Lunar-Year-Agent”, since the fifth lunar year of the Qian-long Reign is an instance of the class of Lunar-Year. This agent found the knowledge starting-solar-yearFn(Title, NULL, Qian-long, NULL) = A.D.1736 in the knowledge base, which means that ‘‘The first lunar year of the Qian-long Reign is A.D.1736”. Here, NULL is a null value. (c) Finally, this agent derived nth-title-solar-yearFn(Title, 5, NULL, Qian-long, NULL) = A.D.1740 by employing the transformation axiom TCT1 in Section 3.3.2.3. Thus, our QA system answered ‘‘A.D.1740”. (5) The question ‘‘Which lunar year in the sixty year cycle is A. D.2010?” is an example of the fifth type of questions. (a) First, the question was transformed into the formula ‘‘stembranch-no(A.D.2010, lunar year, X)”. (b) Then, our QA system called the agent ‘‘Solar-Year-Agent”, because A.D.2010 is an instance of the class of Solar-Year. This agent inferred stem-branch-no(A.D.2010, lunar year, 27) by applying the transformation axiom TCT3 in Section 3.3.2.4, which shows that ‘‘the stem-branch combination representation of A.D.2010 is the 27th stem-branch combination”. (c) Finally, this agent got Index-stem-branch(Geng-yin, 27) according to Table 1 in Section 3.3.2.1, that is, ‘‘the 27th stem-branch combination is Geng-yin”. Hence, our QA system outputted ‘‘Geng-yin Lunar Year”. In summary, since DAML, OWL, KSL, KIF, Cyc, and our time ontologies all specify the topological temporal relations; they can answer the first type of questions. However, the taxonomy of classes of temporal entities with classification criterions, the properties of the intersection of class, and axioms of temporal entities are not constructed in DAML, OWL, KSL, KIF, and Cyc ontologies. These five ontologies are built based on the Gregorian calendar, and do not address the issues about time ontologies based on different calendars and the transformation between temporal entities in different timing systems. Therefore, the latter four types of questions could not be answered by these five ontologies. In addition, it is worth pointing out that our constructed Chinese time ontology can be applied to web services. In other words, it is capable of describing the temporal content of web pages and the temporal properties of web services. Here, we take the following example to illustrate this fact. To describe web services, we employ Ticket.com to demonstrate how our ontology supports OWL-S, which is a web service ontology based on the Web Ontology Language OWL [6,46]. Ticket.com is a fictitious ticket selling service site. A definition of an output parameter CollectTicketTime is shown in Fig. 7, and it specifies when users can collect tickets. CollectTicketTime has two properties EarliestCollectTicketTime and LatestCollectTicketTime that denote the earliest time and the latest time of collecting tickets for users, respectively. The ranges of these two properties are instances of the class Individual of Time Instant. The cardinalities for both properties are all one, which means that an instance of CollectTicketTime must have one and only one attribute value for each property. The values of EarliestCollectTicketTime and LatestCollectTicketTime are equal to PayTicketTime and MatchTime, that are times when users pay tickets and when matches begin, respectively.
5. Discussion We will explain how our development method of the Chinese time ontology could be used to build other time ontologies based on different calendars, and the reasons that our time ontology is significant and useful for other time ontoloiges construction.
C. Zhang et al. / Knowledge-Based Systems 24 (2011) 1057–1074
Fig. 7. A Definition of an output parameter CollectTicketTime.
Given any calendar c, e.g. the Hebrew calendar, the time ontology based on c can be constructed according to the following steps, as shown in Fig. 8. First, take our base time ontology as the base time ontology in the Hebrew time ontology. That is, the time system, the timing system, and the timing ontology within our base time ontology can be utilized as the model for time structure, temporal relations, the computation and representation of time, and classes of temporal entities and their relationships between these classes in the Hebrew time ontology. In this work setting, the Gregorian timing system can also be shared as the ‘‘time intermediator”. Then, develop the Hebrew timing system based on the Hebrew calendar according to the definition of the timing system, that is, time units, operations, functions, and axioms about the instants and intervals in the Hebrew calendar. Here, those axioms need to specify starting instants, ending instants, and duration lengths of calendar intervals. Finally, build the representing method for temporal entities in the Hebrew timing system, and the transformation method
The Time System Our Chinese Time Ontology
between temporal entities in the Hebrew timing system and entities in the Gregorian timing system. By following the methodology presented in this paper, this step will construct various representations of different kinds of temporal entities and their combined representations, and mapping relations between temporal entities in the Hebrew timing system and those in the Gregorian timing system. Thereby, the Hebrew ontology will have been built and can be used to represent and reason with temporal information described in Hebrew ways. The reasons that our time ontology is significant and useful for other time ontoloiges construction are given as follows. (1) The time system, the timing system, and the time ontology in the base time ontology can be employed independently or jointly as the foundation of other time ontologies for different purposes. (a) The time system gives two time primitives and all kinds of topological relations between time primitives with the least predicates, functions, and axioms, following the design criterion of ontology: minimal ontological commitment. So, the topological temporal relation between any two temporal entities can be represented by predicates, functions, and axioms in the time system. (b) The timing system provides a uniform model for various calendars and temporal expressions based on these calendars. It builds a formal model for starting times, ending times, and duration lengths of time units and their relationships. Thus, the timing system constitutes a bridge of transformation between any two temporal entities expressed based on different calendars. (c) The timing ontology builds temporal concepts and their attributes, relationships, and axioms, and the hierarchical taxonomy of temporal concepts with explicit criterions for concept classifications. The timing ontology is constructed following the seven-step method, which is the most mature method of building ontology [45]. Therefore, its respective parts can be selectively used for different temporal information applications. (2) In the process of building our time ontology, our approach meets the criteria of ontology development: clarity, extendibility, and minimal ontological commitment. Hence, our method can be reused to construct other time ontologies based on different calendars. (3) Within the issue about temporal representation and transformation, the divide and conquer technique is independent of any calendar and representative orders of different time units in different calendars. So it can be used to represent different granularities of temporal entities in other time ontologies and transform any two temporal entities in different time ontologies based on different calendars.
The Traditional Chinese Timing System
The Timing System The timing Ontology
The Gregorian Timing System
The Time System Hebrew Time Ontology
The Timing System The timing Ontology
The Hebrew Timing System
Axioms about the Traditional Chinese Calendar Intervals and Instants Representation of Temporal Entities based on the Traditional Chinese Calendar Axioms about the Gregorian Calendar Intervals and Instants Representation of Temporal Entities based on the Gregorian Calendar
Axioms about the Hebrew Calendar Intervals and Instants Representation of Temporal Entities based on the Hebrew Calendar
Fig. 8. An example of building other time ontologies.
Transformation
Transformation
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6. Conclusion In a nation with a long history, the time ontology is generally not purely based on the Gregorian calendar; therefore a more general conceptual model is necessitated in developing a time ontology for the Semantic Web and knowledge processing. In this paper, we introduced, in two steps, Chinese time ontology for the web services and knowledge systems involving temporal entities or properties. In the first step, we developed a base time ontology. The base time ontology includes a time system, a timing system, a timing ontology and a Gregorian timing system. The time system describes the time primitives, the time structure, and the topological relations between instants, intervals and events. The timing system provides a formal uniform model for a variety of specific timing systems. The timing ontology gives an explicit conceptual model for different kinds of temporal entities and their relations. In the second step, we introduced the other parts of the Chinese time ontology with the base time ontology as the basic and integral part: temporal measurement and representation in Chinese ways,
and transformation between temporal entities in the Gregorian and those in the traditional Chinese timing systems. As a result, our method of time ontology development could be used to build other time ontologies, and especially the base time ontology can be reused for other time ontologies. Acknowledgements The work is supported by two grants from the National Natural Science Foundation of China (#60705022 and #61035004) and a grant from the Ministry of Science and Technology (#2001CCA03000). The third author is also supported by the National 973 Project of China (#G1999032701) and the National Key Laboratory of Software Development Environment. Appendix A. Vocabulary of traditional Chinese calendar The table summarizes the vocabulary of traditional Chinese calendar, which is used in the paper.
Chinese Character Pronunciation
Explanation
Chinese Name
Chinese Character Pronunciation
Explanation
Chinese Name
Ai-xin-jue-luoMin-ning
An emperor’s name
Ri-zhong
A Shi-chen
日中
Bing Bu-shi Chen Chen-shi Chou Chou-shi
The 3rd celestial stem A Shi-chen The 5th terrestrial branch A Shi-chen The 2nd terrestrial branch A Shi-chen
爱新觉罗 旻宁 丙 哺时 辰 辰时 丑 丑时
Ren-ding San-geng Shen Shen-shi Shi-chen Shuo
人定 三更 申 申时 时辰 朔
Da-he Ding Ding-mao
An emperor’s reign title The 4th celestial stem A combination of Ding and Mao A Shi-chen A time unit
大和 丁 丁卯
Shi-shi Si Si-geng
A Shi-chen A Shi-chen The 9th terrestrial branch A Shi-chen A time unit The first lunar day of a lunar month A Shi-chen The 6th terrestrial branch A Shi-chen
二更 更
Si-shi Wang
庚 庚子
Er-geng Geng Geng Geng-zi Gui Gui-hai Hai Hai-shi Hua-jia Huang-hun Hui Ji-ming Ji Ji Jia Jia-zi Mao Mao Ze-dong Mao-shi Ping-dan Qian-long Qing Dynasty Ren Ri-die Ri-chu Ri-ru
The 7th celestial stem A combination of Geng and Zi The 10th celestial stem A combination of Gui and Hai The 12th terrestrial branch A Shi-chen A time unit A Shi-chen The last lunar day of a lunar month A Shi-chen The 6thcelestial stem A time unit A celestial stem A combination of Jia and Zi The 4th terrestrial branch The founder of modern China A Shi-chen A Shi-chen The reign title of an emperor A Chinese dynasty The 9th celestial stem A Shi-chen A Shi-chen A Shi-chen
食时 巳 四更 巳时 望
Wei Wei-shi
A Shi-chen The 15th lunar day of a lunar month The 8th terrestrial branch A Shi-chen
癸 癸亥
Wen-zong Wu
An emperor’s title The 5th terrestrial branch
文宗 午
亥 亥时 花甲 黄昏 晦
Wu Wu-shi Wu-geng Tang Dynasty Xin
The 7th celestial stem A Shi-chen A Shi-chen A Chinese dynasty The 8th celestial stem
戊 戊时 五更 唐朝 辛
鸡鸣 己 纪 甲 甲子
Xu Xu-shi Xuan-tong Xuan-zong Ye-ban
The 7th terrestrial branch A Shi-chen An emperor’s reign title An emperor’s title A Shi-chen
戌 戌时 宣统 宣宗 夜半
卯 毛泽东
Yi Yi-geng
The 2nd celestial stem A Shi-chen
乙 一更
卯时 平旦 乾隆
Yin Yin-shi You
The 3rd terrestrial branch A Shi-chen The 10th terrestrial branch
寅 寅时 酉
清朝 壬 日昳 日出 日入
You-shi Yu-zhong Zi Zi-shi
A Shi-chen A Shi-chen The 1st terrestrial branch A Shi-chen
酉时 隅中 子 子时
未 未时
1074
C. Zhang et al. / Knowledge-Based Systems 24 (2011) 1057–1074
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