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A multidimensional knowledge structure
Expert Systems With Applications,Vol. 9, No. 2, pp, 177-187, 1995 Copyright © 1995 Elsevier Science Ltd Printed in the USA. All fights reserved 0957-4174/95 $9.50 + .00
Pergamon 0957-4174(94)00060-3
A Multidimensional Knowledge Structure PAUL K. O. CHow Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong
DANIEL S. YEUNG Departmentof Computing,HongKongPolytechnicUniversity,Kowloon,HongKong
Abstract--Expert system has gone through several shifts in view, from search-based to knowledge-based problem solving and from knowledge transfer to knowledge modeling. However, knowledge is still mostly treated informally. There are widely different opinions on its nature. This paper first attempts to characterize knowledge contents within the context of knowledge level and then proposes a knowledge structure. Four characteristics of knowledge, namely particularity, specificity, bipolarity, and orthogonality, are identified. They form the components of a multidimensional knowledge structure that constitutes a static spatial organization of knowledge. These components are related together through multiple levels of details and multiple system views. The proposed structure creates a taxonomy for classifying knowledge. It brings chaos to order by giving meanings to the phenomenon of diverse opinions on knowledge.
terized? Is there a structure for knowledge and if so what is the structure? There are as yet no convincing answers to these questions. There are various attempts to analyze and structure knowledge. Breuker and Wielinga (1987) propose, as foundations for the KADS methodology, five levels of knowledge analysis that include linguistic, conceptual, epistemological, logic, and implementation, These levels closely parallel the other five levels of knowledge representation and abstraction described by Brachman (1979) in semantic networks. Ontological analysis presents another knowledge level analysis (Alexander et al., 1988). This approach structures domain knowledge into three categories of static, dynamic, and epistemic ontologies. It also describes a system in terms of entity, relation, and transformation. A few have used the term "structure" in describing knowledge. Rauch-Hindin (1988) notes the presence of structure in knowledge. Based on a progress perspective, Gaines, Rappaport, and Shaw (1992) define four types of knowledge structuring: informal, structured, formal, and computational knowledge. This classification transforms knowledge from a domain problem to a knowledge structure suitable for computer implementation. Lastly, Parsaye, and Chignell (1988) define the quality for a basic knowledge structure. Knowledge has been a subject pursued for a long time in many disciplines. In AI/ES, this importance is also
1. INTRODUCTION IN ITS RELATIVELYshort history, artificial intelligence (AI) has already gone through several shifts in view in problem solving. From a search-based method, AI moves to a knowledge-based approach to solve a problem. Knowledge occupies one of the central roles in expert systems (ES) and is the primary source of competence to AI/ES solutions (Feigenbaum, 1977). With the knowledge principle, together with incorporation of the breadth hypothesis (Lenat & Feigenbaum, 1991), acquisition, representation, and sharing of knowledge have since become inmportant issues in AI/ES research. This knowledge transfer view (e.g., Davis, 1979), however, is shifting to a knowledge model view (e.g., Wielinga, Schreiber, & Breuker, 1992). ES is no longer regarded as a container of knowledge transferred from the domain expert. Knowledge modeling is to be used as an effective means to tackle complexity in systems development. In order to adequately model knowledge, a clear understanding on the nature of knowledge is essential. But what is knowledge? How should knowledge be charac-
Requests for reprints should be sent to Paul K. O. Chow, Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong. E-mail: [email protected]
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TABLE 1 Characterization of Knowledge as Type
2 Types
3 Types
4 Types
5 Types
8 Types
Know-what Know-how
Surfaceknow. Domainknow. Deep knowledge
Rule Categoricalknow. Definitional k. Causal know.
Declarative know.
Object Assertion Concept Relation Algorithm Strategy
Procedural know. Heuristic
Commonsense k. Informed commonsense know.
Heuristic Meta-knowledge
reflected in observing the term being frequently mentioned in the literature. Though of premier importance, knowledge is often used in vague ways and has been treated with less vigor than it should have been. Just as Newell (1982) has observed, "knowledge has been treated only informally and gets little play, with representation occupying the centre stage." Knowledge is an abstract concept, arousing many different opinions. As pointed out by Shaw and Woodward (1993), "knowledge cannot be considered unidimensional." Knowledge is multifaceted, defined as types, components, levels, etc. These widely different characterizations on the contents of knowledge indicate that our understanding on knowledge nature should be standardized. Knowledge Level (Newell, 1982) is a level that describes the contents of knowledge and the way knowledge is to be used within a four-level framework. This is in contrast to the lower symbol level, which is concerned with formalism to represent knowledge. At the symbol level, decisions are made about methods to represent symbolic knowledge and to design symbolic data structures. Distinction of these two independent levels allows us to focus on the structure and content of knowledge at the knowledge level. These two levels correspond to the information processing and implementation levels (Chandrasekaran, 1986). Newell's proposal helps to put into context and provides a perspective to guide efforts in characterizing knowledge contents. Given the conceptual contribution of the Knowledge Level, one of its criticism is the potential computational inadequacy, with no full details on control provided. Within the framework of Newell's Knowledge Level, this paper proposes a knowledge structure to characterize the contents of knowledge. The structure abstracts the multilevel and multiview characteristics of knowledge. These two together constitute the multidimensional knowledge structure, derivable from four knowledge attributes identified in this paper, namely particularity, specificity, bipolarity, and orthogonality, The ES that takes this structure adopts multiple system views and incorporates multiple hierarchical levels. This paper assumes that knowledge has structure. And the concept of knowledge is to be restricted within AI/ES discussion, in other words, knowledge for use by computers.
In the next section, we analyze and synthesize various definitions put forward in the literature in an effort to characterize knowledge contents. In the process, different veiws are rectified and consolidated into four knowledge attributes to be discussed in Section 3. Based on this, a knowledge structure is proposed in Section 4. Section 5 presents a discussion of the multidimensional knowledge structure in relation to selected AI/ES research areas at the symbol level.
2. CHARACTERIZATION OF KNOWLEDGE CONTENTS Opinions on the nature of knowledge differ in many ways, reflecting widely different viewpoints. These opinions share similarities as well as differences.
2.1. Domain and Control Knowledge One common distinction made on knowledge is domain and control knowledge, based on the separation of the knowledge base and inference engine in the expert system. Domain knowledge specifies what a system knows about a domain. Control knowledge is concerned with how the system uses what it knows, specifically on ordering of tasks and encoding of problem-solving skill. Introduction of task analysis into knowledge acquisition brings in another kind of knowledge, the task knowledge. Strategic knowledge, which is to define problem-solving control strategies, is another type. The KADS methodology (Wielinga, Schreiber, & Breuker, 1992) proposes as its core a 4-layer structured expertise model. These four hierarchical layers comprise domain, inference, task, and strategy knowledge, with task knowledge being the prime knowledge type among the four. Although they are being labeled as four levels of knowledge, these four can be grouped under two general categories of domain and control knowledge.
2.2. Type of Knowledge Probably the most common attempt to characterize knowledge is to classify knowledge into different types. This classification by type results in different numbers,
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ranging from two to as many as eight (Table 1). For example, Beerel (1988) suggests two types, know-what and know-how. Essentially these should correspond in meaning to declarative and procedural knowledge, which describe the what and how portions of ES. There are suggestions of three knowledge types, surface, domain, and deep knowledge (Harmon & Sawyer, 1990), and four structural types, rule to describe shallow knowledge, and categorical, definitional, and causal knowledge together to represent deep knowledge (Wiederhold, Blum, & Walker, 1986). Surface knowledge describes surfacelevel information. Deep knowledge represents internal structure, including structural and causal relationships. Tuthill and Levy (1991) proposes five types: declarative on what things do, procedural knowledge on how things work, heuristic as rules of thumb, commonsense knowledge to describe general problem-solving knowledge, and finally informed commonsense knowledge to describe general knowledge specific to a particular environment or task. The list can go on. Lauriere (1990) has come up with the most detailed classification. He suggests eight types of knowledge, ranging from object, assertion, concept, relation, rule, algorithm, and strategy to heuristic and meta-knowledge. Meta-knowledge is knowledge about knowledge and is concemed with organizing a body of knowledge. 2.3. Additional Characterization Other terminologies have been adopted besides "type" or "kind," including component, relationship, function, and level (Table 2). Parsaye and Chignell define five elementary components for knowledge: naming, describing, organizing, relating, and constraining. Hayes-Roth, Waterman, and Lenat (1983) and Harmon and Sawyer also describe knowledge to comprise different components, although they quote different contents and use different terms for these knowledge components. The three components of Hayes-Roth et al. contain description, relationships, and procedures. Harmon and Sawyer explicitly define the concept of relationships and view knowledge as relationships between objects. In short, knowledge is abstracted into two types. First, declarative knowledge consists of declarative relationships, which include logical and empirical relationships. Secondly, procedural knowledge specifies procedural relationships. Other authors, such as Rauch-Hindin (1988) and Deben-
ham (1989), also describe knowledge as relationship or association. Rich and Knight (1991) argue that knowledge serves two functions in AI programming. The first is essential knowledge that defines what can be done to solve a problem and what it means to have a problem solved. Secondly, heuristic knowledge states how best to go about solving a problem efficiently. Depending on the degree of accounting for principles and relationships, Parsaye and Chignell use levels of knowledge to distinguish shallow knowledge from deep knowledge. There are other characterizations of knowledge. McGraw and Harbison-Briggs (1989) state that knowledge can exist in many forms. They categorize knowledge into episodic, semantic, declarative, and procedural knowledge. Episodic knowledge describes long-term episodes or events, along with temporal-spatial relations among these events. Semantic knowledge reflects structure, organization and representation, and, like episodic knowledge, is long-term in nature. Abstraction is an important attribute of knowledge. Both Liebowitz and Lightfoot (1993), and Wiederhold include abstraction in characterizing knowledge. Wiederhold even extends abstraction to include generalization. 2.4. Declarative and Procedural Knowledge In sum, declarative and procedural knowledge seem to be the more common choices among authors. Description and relation, proposed by Hayes-Roth et al., belong to declarative knowledge. Fact and concept, proposed by Tuthill and Levy, is also part of declarative knowledge. Essential knowledge, proposed by Rich and Knight, is declarative knowledge as it describes what a system does. Essential knowledge of Rich and Knight, and definitional and categorical knowledge of Wiederhold, correspond in meaning to declarative knowledge proposed by Tuthill and Levy. Rule and causal knowledge, proposed by Wiederhold, is similar to procedural knowledge of Harmon and Sawyer. Algorithm and step, proposed by Lauriere, are part of procedural knowledge. Tuthill's definition on procedural knowledge specifies how things work, or "know-how," which is in some sense related to heuristic knowledge described by Rich and Knight. But, the former describes procedure as method and implies more than the best method (assisted with heuristics to reduce search space) as defined by the latter. It is regarded that heuristic is part of procedural
TABLE 2 Additional Characterization of Knowledge
Component (1)
Component(2)
Relationship
Function
Naming Describing Organizing Relating Constraining
Description Relationship Procedure
Declarativeknow. Essential know. Proceduralknow. Heuristicknow.
Level Shallow know. Deep knowledge
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Level of Details Domain / ControlKnowledge - KnowledgeContents Declarative/ Procedural Knowledge - KnowledgeFormats Fact, Concept,Relation/ Rule, Step, Algorithm,Strategy - DetailedKnowledgeItems
FIGURE 1. ParUculaflty. knowledge which includes method, step and procedures. Heuristic is to mean guidelines on how best to apply knowledge, using Rich's definition, although some other authors regard heuristic to be another type of knowledge by itself. It is often regarded mistakenly that domain knowledge is declarative and control knowledge is procedural. Van Harmelen (1991) has made an attempt to rectify this confusion. As argued by Van Harmelen, domain knowledge embodies contents of a problem domain whereas declarative knowledge is more concerned with the format written down. Domain knowledge can be written down in the format of either declarative or procedural knowledge. Likewise, control knowledge can also be written down in either declarative or procedural knowledge. In other words, both domain and control knowledge can be formulated as either one or both. For example, domain knowledge can be formulated, declaratively as logic, or procedurally as production rules. However, control knowledge can be either domain dependent or domain independent, but domain knowledge is usually domain dependent. 3. KNOWLEDGE ATTRIBUTES By consolidating all the different views presented in the previous sections, four knowledge attributes are identified. These four characteristics of knowledge, which constitute important ingredients for the multidimensional knowledge structure, are particularity, specificity, bipolaxity, and orthogonality. 3.1. Particularity
Particularity represents levels of detail. It is the quality of being particular and detailed. Generality and particularity form two extremes on a vertical continuum of multiple levels of detail. Lauriere's eight types of knowledge provide a useful classification framework for particularity. The three items of fact, concept, and relation can be grouped as detailed particulars of the declarative knowledge. The other four items (rule, step, algorithm, and strategy) belong to details of procedural knowledge (Figure 1). These descriptions of declarative and procedural knowledge are similar to proposals by Hayes-Roth
1
et al. (1983), Tuthill and Levy (1991), and Harmon and Sawyer (1990) as described in Section 2. Although both domain and declarative knowledge represent what a system knows, domain knowledge, as pointed out by Van Harmelen (1991), embodies contents of a problem domain whereas declarative knowledge is concerned with the format written down. Domain/control knowledge and declarative/procedural knowledge are assigned to two separate levels with different degree of particularity. 3.2. Specificity
Domain specific is a term frequently used in expert systems. Specificity is the depth of relationship with one particular problem domain. This quality can be described in terms of domain and control knowledge. Domain knowledge is dependent on and specific to a domain; control knowledge can be either domain dependent or domain independent. This implies that control knowledge is not specific to any one domain, though at the same time it does not apply to every domain. Thus, control knowledge is less specific, or has a lower degree of specificity, than domain knowledge. Conversely, we can also say that control knowledge has a wider scope of applicability, or a higher degree of generality, than domain knowledge (Figure 2). Specificity also applies to informed commonsense knowledge and commonsense knowledge, as described by Tuthill and Levy. Informed common sense has a higher degree of specificity than general commonsense knowledge as it is general knowledge specific to a particular environment. This pair of informed and general commonsense knowledge is more general than the pair of domain/control knowledge as the former is general knowledge. There are other cases that form pairs of generality versus specificity. Semantic memory knowledge is the organization of facts into hierarchy and is not connected to personal experience. This is a type of general knowledge. Episodic knowledge, on the other hand, is the selection from personal experience that belongs to a specific situation, and this is specific knowledge. In another case, deep knowledge (as described by Wiederhold, for example) is applicable to various situations and thus is general in nature. Whereas
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Specific z ~x
Domain Knowledge - Domain-Specific Control Knowledge - Either Domain-Dependent or Domain-lndependent hfformed ComlnonsenseKnowledge - General, but Specific to a Particular Environemnt CommonsenseKnowledge - General
General FIGURE 2. Specificity.
shallow knowledge applies to a particular domain and so is specific, extensional knowledge is the set of all things denoted by a given concept. It generalizes concept and is general knowledge. Intensional knowledge determines what a specific concept means and is specific. All these are examples that form pairs of generality versus specificity.
3.3. Bipolarity Bipolarity represents two views of an entity. We make use of this dual-view quality to characterize knowledge into pairs (Figure 3). This is analogous to viewing the two sides of one coin. The pair of declarative and procedural knowledge is an example of bipolarity. On one side is know-what, as coined by Beerel, which constitutes fact, concept, and relation. The other side includes know-how, which comprises rule, step, algorithm, and strategy. Whether knowledge is declarative or procedural depends on viewpoint. This knowledge can be represented at the symbol level using logic or production rule. Domain and control knowledge are another pair that exhibits bipolarity. Domain knowledge is typically domain dependent whereas control knowledge can be either domain dependent or domain independent. These tw6 pairs are seen as equivalent to two poles on a horizontal axis, forming a bipolarity. These two views are coexisting and complementary, and not mutually exclusive of each other. Bipolarity implies that knowledge is interchangeable in format. The two attributes of specificity and particularity can also be regarded as bipolarity cases, as particularity and generality constitute two poles of an axis, this time a vertical axis. Likewise, the same applies to specificity versus generality.
3.4. Orthogonality There seems to be a paradox of "What versus How" with the two pairs of domain/control knowledge and declar-
ative/procedural knowledge. Both domain and declarative knowledge represent what a system knows, and both control and procedural knowledge are concerned with how a system uses what it knows. How can these two pairs be related together? And how can they be integrated and used together within a framework? As Van Harmelen has stated, domain/control knowledge differs from declarative/procedural knowledge in content versus format, and Davis (1993) indicates clues for the dilemma by saying "one person's floor is another person's ceiling." The paradox can be resolved by regarding these two pairs as orthogonal to each other. As shown in Figure 4, the two pairs can be arranged at right angles and are mutually perpendicular to each other, forming an orthogonality. This orthogonal arrangement indicates that contents of domain knowledge can be written in either declarative or procedural format. Fact, concept, and relation of declarative knowledge form part of the domain knowledge. Rule, step, algorithm, and strategy of procedural knowledge form the other part of domain knowledge. And the same applies to control knowledge. 4. A NEW K N O W L E D G E S T R U C T U R E The four knowledge attributes described in Section 3 serve as important components for the proposed multidimensional knowledge structure. It is multidimensional in nature because it assumes several measurements: hierarchical level and system view. Knowledge structure, as defined by Davis (1993), is a structured collection of concepts and their interrelationships. The two dimensions, derived from the four attributes, constitute the structured and related components of the structure. 4.1. Multilevel Structure The first dimension of the knowledge structure proposal is hierarchical in nature, forming a multilevel structure. Knowledge items are organized into levels and are related together through hierarchical relationships. The
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(a)
DomainKnowledge
ConWolKnowledge
Gen-Part substructure can be embedded into the Gen-Spec substructure. Thus, these two knowledge substructures are linked through an embedding relationship.
Venus
ProceduralKnowledge
DeclarativeKnowledge
~)
VS.
l)eCl~t~tl'~,e . rt~°~,l~tge
Gen-Part Substructure. Gen-Part knowledge substructure includes generality versus particularity. It describes knowledge contents by level of particularity, represented in a range descending from general to detail. Generality and particularity constitute two vertical bipolars in this knowledge structure. Figure 1 embodies the Gen-Part structure. Gen-Spec Substructure. Gen-Spec knowledge substructure includes generality versus specificity. Level of specificity is applied in this structure. The structure embodies knowledge, which ranges from general to domain-specific knowledge. Generality and specificity form another two vertical bipolars. Figure 2 embodies the Gen-Spec structure. 4.2. M u l t i v i e w Structure
VS.
The multiview knowledge structure adopts the multiple system views as the second dimension. It incorporates two knowledge attributes, bipolarity and orthogonality. Bipolarity allows a piece of knowledge to be seen from two sides. As described in Section 2, knowledge can be viewed either declaratively or procedurally. These two bipolar views constitute the basic structural unit in our
(c)
,.~
~
FIGURE 3. Bipolarity.
multilevel structure implies that there are multiple levels within the knowledge level. These multiple levels of abstraction are needed to consolidate complex domain details. Leveling helps to focus attention at issues appropriate to current level of abstraction within the knowledge level. It also assists to ignore complexity hidden at the lower symbol level. The multilevel structure incorporates two knowledge attributes, particularity and specificity, and is composed of two substructures, Gen-Part and Gen-Spec substructures. The
FIGURE 4. Orthogonality.
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Specific l~,arrow Domain
Principle
Far-Flung Domains BreadthHypothesis
FIGURE 5. Pyramid for narrow and far-flung domains.
knowledge structure. This knowledge structuring primitive, consisting of both declarative and procedural knowledge, is used as the basic building block for creating knowledge structure (Figure 3). Orthogonality allows multiples of bipolar views to be integrated, a sort of multiple of multiple views. As Van Harmelen points out, contents of domain and control knowledge can be formatted as declarative and/or procedural knowledge. A chunk of knowledge, composing domain and control knowledge, would also comprise declarative and procedural descriptions (Figure 4). This characteristic of knowledge is depicted as two pairs of bipolar views being arranged orthogonal to each other. Figures 3 and 4 together constitute the multiview structure. It should be noted that multiview structure also embodies the GenPart structure with different levels of abstraction as described in the previous section. In this sense, both multilevel and multiview structures are tightly integrated together.
4.3. Multidimensional Knowledge Structure From particularity to specificity and from bipolarity to orthogonality, the merging of multilevel and multiview structures gives rise to the multidimensional knowledge structure. Hierarchical levels and system views from the two dimensions. At the detailed knowledge items level, declarative knowledge can be broken down into particulars of fact, concept, and relation. Procedural knowledge comprises rule, step, algorithm, and strategy. At the knowledge format level, declarative and procedural knowledge together form two complementary views of knowledge. At the knowledge content level, domain and control knowledge can both be described with either declarative or procedural knowledge. It can
be seen from the structure that knowledge building is a continuous and recursive abstraction process, from lower level particularity to higher level generality and also from higher level specificity to lower level generality, and vice versa. This is in conformance with the interative, prototyping approach in ES development. All these knowledge descriptions are specific to a domain. Accumulation of multiple domain-specific knowledge contributes to the building of general knowledge. The wide base of the pyramid in Figure 5 represents this desired characteristic of generality. General common sense knowledge overcomes the brittleness shortcoming of the first era expert systems (Lenat, Prakesh, & Shepherd, 1986). This can, in the words of Feigenbaum (1992), "create a parachute for a soft fall by using more general knowledge of a nonspecialist sort to do some kind of problem solving when the detailed expert knowledge is lacking." It should be noted that general knowledge also incorporates the basic knowledge structuring unit that is described in multiview knowledge (Figure 6). In sum, what we have produced is a spatial organization of knowledge. This static structure describes the positional relationships among different facets of knowledge.
4.4. Comparison to Other Knowledge Structures Many authors have incorporated multiple levels of abstraction in classifying problems. Examples include Clancey's heuristic classification on problem solving (1985) and Chandrasekaran's hierarchical classification on generic tasks (1986). We classify knowledge not just by level, but also by view. This constitutes the most important difference between our work and others. Shaw and Woodward (1990) describe three dimensions of
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knowledge, view, knowledge type, and level. These three dimensions together share some similarities to our multilevel and multiview proposal. Yeh and Zave (1980) identify three structuring primitives, namely partitioning, abstraction, and projection. Partitioning and abstraction capture the structural relations of aggregation and generalization, respectively. Projection corresponds to a view of the structural relation. Projection is similar to the bipolar and orthogonal views we previously describe. However, our system view is derived from bipolarity, whereas orthogonality allows for multiple dual views. In a sense, multidimensional analysis in knowledge acquisition shares some similarities with the knowledge structure in terms of its dimensions. The card sort technique, which belongs to multidimensional analysis, uses factor (overall scale) and level (card piles) as the two dimensions. Level is similar to our multilevel structure, but factor is not. Our research concurs with Rauch-Hindin that structure is present in knowledge. However, we differ from the knowledge structuring primitives that Brachman (1979) has proposed at the epistemological level. The KADS approach views knowledge modeling as the major challenge. We regard that characterization of knowledge contents is a high priority item. 5. TIMETABLING APPLICATION This section describes a timetabling expert system (Martinson, Kwan, Chow, & Lo, 1993) that is applied with the knowledge attributes and structures presented in Sections 3 and 4. Academic timetabling, as a kind of scheduling, is one of the more important and complex administrative activities in formal education. In larger institutions, such activities are often consolidated and
assigned to a group of individuals, the schedulers. Timetabling represents the allocation of scarce time and room resources for study programmes subject to the constraints and preferences of teachers and students. The traditional method for creating academic timetables is through the manual approach, which is time consuming and tedious. Such characteristics would make this domain an ideal candidate for computerization. A variety of computerization approaches have been attempted. This includes simulated manual processing, graph theory, optimization, etc. However, the complexity of programmes and resources, together with the constraints imposed, make satisfactory solutions difficult. A knowledge-based approach provides a new dimension to tackle the timetabling problem. In the academic environment, for which the Timetabling Expert System is developed, scarcity of time is of particular concern for the part-time evening study programme. Part-time students are required to come for lessons on only three evenings per week with a normal load of two to three subjects. However, there are only three teaching hours in each evening. There is a need to schedule classes in all the available teaching timeslots on those three evenings. This constitutes the tightest constraint from the student side. The schedulers' knowledge to get around this constraint of scarcity in timetable timeslots is modeled. These many facets of knowledge related to the constraint are organized into domain/ control knowledge, declarative/procedural knowledge, and detailed knowledge items, as sampled in Table 3. The two pairs of domain/control knowledge and declarative/procedural knowledge form two separate bipolars and represent different ways of viewing timeslot scarcity constraint at both content and format levels. These two are broken down into detailed knowledge items, such as
Narrow Domain
Far-Flung Domains
FIGURE 6. Multidimensional knowledge structure.
Multidimensional Knowledge Structure
185 TABLE 3 Sample Tlmetabllng Knowledge
Knowledge content • Domain knowledge Constraint on timeslot scarcity (Specific to timetabling domain) • Control Knowledge "lqmeslot selection (Timetabling dependent) Forward chaining, backward search (Timetabling independent) Knowledge format • Declarative Knowledge Fixed number of timeslots in timetable • Procedural knowledge Timeslot selection policy Timeslot priority scheme as constraint satisfaction strategy Updating of selected timeslots to student data base Detailed knowledge items • Fact: Timeslot, timetable, priority value, student (class) • Concept: Choosing a suitable timeslot • Relation: Positional relations between different timeslots
• Rule: lqmeslot selection rules, conflict relief rules • Step: Sequence of timeslot (& room) selection followed by conflict relief • Algorithm: Update selected timeslot to student data base file • Strategy: Scheme to assign priority value to timeslots in student's timetable
timeslot, conflict relief rule, priority scheme, etc. The three levels are arranged in a knowledge hierarchy, the Gen-Part structure, representing different degree of particularity. The two pairs of bipolars form orthogonality as shown in Figures 3a-c. They also become the multiview knowledge structure. Domain-specific knowledge is essential in being the source of power for solution. However, this domain specificity also creates the brittleness problem. For example, the timetabling expert system is not prepared to handle other constraints such as balancing the interests of different groups, staff, students, etc., so that one is ill-treated in the midst of scheduling conflicts. Automated arbitration knowledge, belonging to another domain, seems far away to be readily helpful. 6. DISCUSSION & CONCLUSION The proposed knowledge structure to characterize the contents of knowledge is specific to Knowledge Level. This section attempts to relate the proposed structure to the lower levels within Newell's 4-level framework, with particular emphasis on the symbol level. Multiplicity in AI/ES is now new. Bobrow (1986) has argued for an adoption of multiple programming paradigms for AI programming. Multiple knowledge representation is not new either. Sloman (1985) proposes that there exists a need for various knowledge representation formalisms and advocates the use of many (or multiple) knowledge representations. Mixed representation formalisms have been used to represent different types of knowledge. For
example, KRYPTON (Brachman, Fikes, & Levesque, 1983) represents definitional and assertional knowledge; KLTWO (Vilan, 1985) uses two different languages to deal with propositional and quantificational reasoning; and KEDE (Zheng & Li 1992) handles as many as five kinds, in addition to mixed reasoning mechanisms. As put forward by Reichgelt (1991), one of the questions to follow this multiple representation argument is when to use which knowledge representations. In an empirical study of knowledge elicitation techniques, Burton, Shadbolt, Hedgecock, and Rugg (1987) conclude that the order of using knowledge elicitation techniques does not make any difference in the quality of knowledge elicited. This clue indicates that the order of establishing declarative and procedural knowledge is not important in creating the primitive knowledge structure. We suggest not to prescribe any procedural sequences in deriving declarative and procedural knowledge, as well as in domain and control knowledge. Gammack and Young (1985) have argued that different knowledge types should be matched to appropriate knowledge acquisition techniques. Like knowledge representation, combined use of knowledge acquisition techniques can be adopted to elicit both declarative and procedural knowledge. As described by McGraw and Harbison-Briggs (1989), interviews are good for eliciting declarative knowledge. Card sort can also be used. Structured interviews, process tracing, simulation, and protocol analysis help in elicitation of procedural knowledge. Laddered grid is a useful technique to develop a hierarchy of knowledge. However, McGraw
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and Seale (1987) caution that use o f these techniques should also be related to development phases. This points to our further work. Expert system as an end-product is a moving target. The proposed knowledge structure better accommodates changes. This is achieved by structuring of knowledge which in turn structures the ES development process. Although this paper emphasizes the need for a knowledge structure, overemphasis on structure results in rigidity. Flexibility in the ES development process should be accounted for balancing against rigidity. Multiplicity allows for built-in flexibility, as extension with more levels and more views is possible. Furthermore, dimensionality can also be incremented. Other possible dimensions include temporal and control. Through this multidimensional framework, flexibility and extensibility enhance ES development. A structure is an important prerequisite for any attempt to scale up expert systems. Knowledge sharing, very large knowledge bases, and large-scale interoperable expert systems are emerging as important research areas. Some pioneering projects include CYC (Guha & Lenat, 1991), for building large-scale general common sense knowledge, and PACT (Cutkosky et al., 1993), for demonstrating the feasibility o f distributed, interoperable knowledge systems. A Knowledge Interface Format (KIF) has been defined for knowledge sharing. More work is needed to explore their relationships to the knowledge structure. Other work includes defining a framework for mapping knowledge attributes and structures to knowledge representation method and knowledge acquisition techniques. Even with the several view shifts already undergone in AI/ES, knowledge is still occupying a central role in ES development. In characterizing knowledge contents within the context of Newell's knowledge level, particularity, specificity, bipolarity, and orthogonality are identified as knowledge attributes. Based on these, a multidimensional knowledge structure composed of multiple levels and multiple views is proposed. As knowledge is the primary source o f competence, structuring knowledge becomes an important prerequisite for any attempts on AI/ES solutions. The major contribution of this static spatial structure is that it describes the positional relationships among different facets of knowledge and gives clarification on the characteristic of knowledge.
References Alexander, J., Freiling, M., Shulman, S., Rehfuss, S., & Messick, S. (1988). Ontological Analysis: an ongoing experiment. In J. Boose, & B. Gaines (Eds.), Knowledge.based systems, voL 2: Knowledge acquisition tools for expert systems (pp. 25-30). New York: Academic Press. Beerel, A. C. (1988). Expert systems in business: A practical guide, Chichester: Ellis Horwood.
Bobrow, D. G. (1986). Multiple paradigms in AI programming, In C. Rich & R. C. Waters (Eds.), Readings in artificial intelligence and software engineering, San Mateo, CA: Morgan Kaufmaan. Brachman, R. (1979). On the epistemological status of semantic networks, In N. Findler, (Ed.), Associative networks, New York: Academic Press. Brachman, R., Fikes, R. E., & Levesque, H. J. (1983). KRYPTON: A functional approach to knowledge representation, IEEE Computer 16(10), 67-73. Breuker, J. A., & Wielinga, B. J. (1987). Use of models in the interpretation of verbal data, In A. L. Kidd (Ed.), Knowledge acquisition for expert systems: a practical handbook, New York: Plenum Press. Burton, A. M., Shadbolt, N. R., Hedgecock, A. P., & Rugg, G. (1987). A formal evaluation of knowledge elicitation techniques for expert systems: Domain 1, In B. Braemer (Ed.), Research and development in expert systems (pp. 136-145). Cambridge: Cambridge University Press. Chandrasekaran, B. (1986). Generic task in knowledge-based reasoning: High-level building blocks for expert system design, IEEE Expert, 1(3), 23-29. Clancey, W. J. (1985). Heuristic classification, Artificial Intelligence, 20, 289-350. Cu~osky, M. R., Engelmore, R. S., Fikes, R. E., Genesereth, M. R., Gruber, T. R., Mark, W. S., Tenenbaum, J. M., & Weber, J. C. (1993). PACT:An experiment in integratingconcurrent engineering systems, IEEE Computer, 26(1), 28-37. Davis, A. (1993). Software requirements: Objects,functions and states, Englewood Cliffs, NJ: Prentice-Hall. Davis, R. (1979). Interactive transfer of expertise: Acquisition of new inference rules, Artificial Intelligence, 12(2), 121-159. Debenham, J. K. (1989). Knowledge systems design, Englewood Cliffs, NJ: prentice-Hall. Feigenbaum,E. A. (1977). The art of artificial intelligence:Themes and case studies of knowledge engineering, In Proceedings of the 5th International Joint Conference on Artificial Intelligence, pp. 1014-1029. Feigenbaum,E. A. (1992). A personal view of expert systems: Looking back and looking ahead, Expert Systems with Applications, 5, 193-201. Gaines, B. R., Rappaport, A. T., & Shaw, M. L. G. (1992). Combining paradigms in knowledge engineering, Data & Knowledge Engineering, 9, 1-18. Gammack, J., & Young, R. (1985). Psychological techniques for eliciting expert knowledge, In B. Braemer (Ed.), Research and development in expert systems (pp. 105-122). Cambridge: Cambridge Univerity Press. Guha, R. V., & Lenat, D. B. (1991). CYC: A mid-term report, A/ Magazine, 11(3), 32. Harmon, P., & Sawyer, B. (1990). Creating expert systems: For business and industry, New York: John Wiley. Hayes-Roth, F., Waterman, D. A., & Lenat, D. B. (1983). Building expert systems. Reading, MA: Addison-Wesley. Lauriere, J. (1990). Problem solving and artificial intelligence, Englewood Cliffs, NJ: Prentice-Hall. Lenat, D. B., Prakash, M., & Shepherd, M. (1986). CYC: Using commonsense knowledge to overcome brittleness and knowledge acquisition bottleneck.,41 Magazine, 6, 65-85. Lenat, D. B., & Feigenbaum, E. A. (1991). On the threshold of knowledge,Artificial Intelligence, 47, 185-250. Liebowitz, J., & Lightfoot, P. (1993). Scheduling approaches in expert systems: A study of their applicability. Expert Systems with Applications, 6, 231-235. Martinson M. G., Kwan, K. C., Chow, P. K. O., & Lo, V. H. Y. (1993). Academic timetabling with a microcomputer-basedexpert system Shell, Journal of Artificial intelligence in Education 4(4), 333-356.
Multidimensional Knowledge Structure McGraw, K. L., & Harbison-Briggs, K. (1989). Knowledge acquisition: Principles and guidelines, Englewood Cliffs, N J: Prentice-Hall. McGraw, K. L., & Seale, M. (1987). Multiple expert knowledge acquisition Methodology: MEKAM, In Proceedings, 3rd Australian Conference on Applications of Expert System, pp 165-197. Newell, A. (1982). The knowledge level, Artificial Intelligence, 18, 87-127. Parsaye, P., & Chignell, M. (1988). Expert systems for experts, New York: Wiley. Rauch-Hindin, W. B. (1988). A guide to commercial artificial intelligence: Fundamentals and real-worM applications, Englewood Cliffs. NJ: Prentice-Hall. Reichgelt, H. (1991). Knowledge representation: An AI perspective, Ablex Publishing Corp. Riche, E., & Knight, K. (1991). Artificial intelligence, New York: McGraw-Hill. Shaw, M. L. G., & Woodward, J. B. (1990). Modeling expert knowledge, Knowledge Acquisition, 2(2): 179-206. Sloman, A. (1985). Why we need many knowledge representation formalisms, In M. Bramer (Ed.), Research and development in
187 expert systems (pp. 163-183). Cambridge: Cambridge University Press. Tuthill, G. S., & Levy, S. T. (1991). Knowledge based systems: A manager's perspective, TAB Book. Van Harmelen, F. (1991). Meta-level inference Systems, London: Pitman. Vilain, M. (1985). The restricted language architecture of a hybrid representation language, In Proceedings oflJCAl, 9, 547-551. Wiederhold, G., Blum, R. L., & Walker, M. (1986). An integration of knowledge and data representation, In M. L. Brodie & J. Mylopoulos (Eds.), On knowledge base management systems, New York: Springer-Verlag. Wielinga, B. J., Schreiber, A. Th., & Breuker, J. A. (1992). KADS: A modeling approach to knowledge engineering, Knowledge Acquisition, !-50. Yeh, R., & Zave, P. (1980). Specifying software requirements, In Proceedings of the IEEE, 68(9), 1077-1085. Zheng, A. J., & Li, W. (1992). A hybrid knowledge engineering development environment (KEDE). International Journal of Artificial Intelligence Tools, 1(4), 463-502.
Pergamon 0957-4174(94)00060-3
A Multidimensional Knowledge Structure PAUL K. O. CHow Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong
DANIEL S. YEUNG Departmentof Computing,HongKongPolytechnicUniversity,Kowloon,HongKong
Abstract--Expert system has gone through several shifts in view, from search-based to knowledge-based problem solving and from knowledge transfer to knowledge modeling. However, knowledge is still mostly treated informally. There are widely different opinions on its nature. This paper first attempts to characterize knowledge contents within the context of knowledge level and then proposes a knowledge structure. Four characteristics of knowledge, namely particularity, specificity, bipolarity, and orthogonality, are identified. They form the components of a multidimensional knowledge structure that constitutes a static spatial organization of knowledge. These components are related together through multiple levels of details and multiple system views. The proposed structure creates a taxonomy for classifying knowledge. It brings chaos to order by giving meanings to the phenomenon of diverse opinions on knowledge.
terized? Is there a structure for knowledge and if so what is the structure? There are as yet no convincing answers to these questions. There are various attempts to analyze and structure knowledge. Breuker and Wielinga (1987) propose, as foundations for the KADS methodology, five levels of knowledge analysis that include linguistic, conceptual, epistemological, logic, and implementation, These levels closely parallel the other five levels of knowledge representation and abstraction described by Brachman (1979) in semantic networks. Ontological analysis presents another knowledge level analysis (Alexander et al., 1988). This approach structures domain knowledge into three categories of static, dynamic, and epistemic ontologies. It also describes a system in terms of entity, relation, and transformation. A few have used the term "structure" in describing knowledge. Rauch-Hindin (1988) notes the presence of structure in knowledge. Based on a progress perspective, Gaines, Rappaport, and Shaw (1992) define four types of knowledge structuring: informal, structured, formal, and computational knowledge. This classification transforms knowledge from a domain problem to a knowledge structure suitable for computer implementation. Lastly, Parsaye, and Chignell (1988) define the quality for a basic knowledge structure. Knowledge has been a subject pursued for a long time in many disciplines. In AI/ES, this importance is also
1. INTRODUCTION IN ITS RELATIVELYshort history, artificial intelligence (AI) has already gone through several shifts in view in problem solving. From a search-based method, AI moves to a knowledge-based approach to solve a problem. Knowledge occupies one of the central roles in expert systems (ES) and is the primary source of competence to AI/ES solutions (Feigenbaum, 1977). With the knowledge principle, together with incorporation of the breadth hypothesis (Lenat & Feigenbaum, 1991), acquisition, representation, and sharing of knowledge have since become inmportant issues in AI/ES research. This knowledge transfer view (e.g., Davis, 1979), however, is shifting to a knowledge model view (e.g., Wielinga, Schreiber, & Breuker, 1992). ES is no longer regarded as a container of knowledge transferred from the domain expert. Knowledge modeling is to be used as an effective means to tackle complexity in systems development. In order to adequately model knowledge, a clear understanding on the nature of knowledge is essential. But what is knowledge? How should knowledge be charac-
Requests for reprints should be sent to Paul K. O. Chow, Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong. E-mail: [email protected]
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TABLE 1 Characterization of Knowledge as Type
2 Types
3 Types
4 Types
5 Types
8 Types
Know-what Know-how
Surfaceknow. Domainknow. Deep knowledge
Rule Categoricalknow. Definitional k. Causal know.
Declarative know.
Object Assertion Concept Relation Algorithm Strategy
Procedural know. Heuristic
Commonsense k. Informed commonsense know.
Heuristic Meta-knowledge
reflected in observing the term being frequently mentioned in the literature. Though of premier importance, knowledge is often used in vague ways and has been treated with less vigor than it should have been. Just as Newell (1982) has observed, "knowledge has been treated only informally and gets little play, with representation occupying the centre stage." Knowledge is an abstract concept, arousing many different opinions. As pointed out by Shaw and Woodward (1993), "knowledge cannot be considered unidimensional." Knowledge is multifaceted, defined as types, components, levels, etc. These widely different characterizations on the contents of knowledge indicate that our understanding on knowledge nature should be standardized. Knowledge Level (Newell, 1982) is a level that describes the contents of knowledge and the way knowledge is to be used within a four-level framework. This is in contrast to the lower symbol level, which is concerned with formalism to represent knowledge. At the symbol level, decisions are made about methods to represent symbolic knowledge and to design symbolic data structures. Distinction of these two independent levels allows us to focus on the structure and content of knowledge at the knowledge level. These two levels correspond to the information processing and implementation levels (Chandrasekaran, 1986). Newell's proposal helps to put into context and provides a perspective to guide efforts in characterizing knowledge contents. Given the conceptual contribution of the Knowledge Level, one of its criticism is the potential computational inadequacy, with no full details on control provided. Within the framework of Newell's Knowledge Level, this paper proposes a knowledge structure to characterize the contents of knowledge. The structure abstracts the multilevel and multiview characteristics of knowledge. These two together constitute the multidimensional knowledge structure, derivable from four knowledge attributes identified in this paper, namely particularity, specificity, bipolarity, and orthogonality, The ES that takes this structure adopts multiple system views and incorporates multiple hierarchical levels. This paper assumes that knowledge has structure. And the concept of knowledge is to be restricted within AI/ES discussion, in other words, knowledge for use by computers.
In the next section, we analyze and synthesize various definitions put forward in the literature in an effort to characterize knowledge contents. In the process, different veiws are rectified and consolidated into four knowledge attributes to be discussed in Section 3. Based on this, a knowledge structure is proposed in Section 4. Section 5 presents a discussion of the multidimensional knowledge structure in relation to selected AI/ES research areas at the symbol level.
2. CHARACTERIZATION OF KNOWLEDGE CONTENTS Opinions on the nature of knowledge differ in many ways, reflecting widely different viewpoints. These opinions share similarities as well as differences.
2.1. Domain and Control Knowledge One common distinction made on knowledge is domain and control knowledge, based on the separation of the knowledge base and inference engine in the expert system. Domain knowledge specifies what a system knows about a domain. Control knowledge is concerned with how the system uses what it knows, specifically on ordering of tasks and encoding of problem-solving skill. Introduction of task analysis into knowledge acquisition brings in another kind of knowledge, the task knowledge. Strategic knowledge, which is to define problem-solving control strategies, is another type. The KADS methodology (Wielinga, Schreiber, & Breuker, 1992) proposes as its core a 4-layer structured expertise model. These four hierarchical layers comprise domain, inference, task, and strategy knowledge, with task knowledge being the prime knowledge type among the four. Although they are being labeled as four levels of knowledge, these four can be grouped under two general categories of domain and control knowledge.
2.2. Type of Knowledge Probably the most common attempt to characterize knowledge is to classify knowledge into different types. This classification by type results in different numbers,
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ranging from two to as many as eight (Table 1). For example, Beerel (1988) suggests two types, know-what and know-how. Essentially these should correspond in meaning to declarative and procedural knowledge, which describe the what and how portions of ES. There are suggestions of three knowledge types, surface, domain, and deep knowledge (Harmon & Sawyer, 1990), and four structural types, rule to describe shallow knowledge, and categorical, definitional, and causal knowledge together to represent deep knowledge (Wiederhold, Blum, & Walker, 1986). Surface knowledge describes surfacelevel information. Deep knowledge represents internal structure, including structural and causal relationships. Tuthill and Levy (1991) proposes five types: declarative on what things do, procedural knowledge on how things work, heuristic as rules of thumb, commonsense knowledge to describe general problem-solving knowledge, and finally informed commonsense knowledge to describe general knowledge specific to a particular environment or task. The list can go on. Lauriere (1990) has come up with the most detailed classification. He suggests eight types of knowledge, ranging from object, assertion, concept, relation, rule, algorithm, and strategy to heuristic and meta-knowledge. Meta-knowledge is knowledge about knowledge and is concemed with organizing a body of knowledge. 2.3. Additional Characterization Other terminologies have been adopted besides "type" or "kind," including component, relationship, function, and level (Table 2). Parsaye and Chignell define five elementary components for knowledge: naming, describing, organizing, relating, and constraining. Hayes-Roth, Waterman, and Lenat (1983) and Harmon and Sawyer also describe knowledge to comprise different components, although they quote different contents and use different terms for these knowledge components. The three components of Hayes-Roth et al. contain description, relationships, and procedures. Harmon and Sawyer explicitly define the concept of relationships and view knowledge as relationships between objects. In short, knowledge is abstracted into two types. First, declarative knowledge consists of declarative relationships, which include logical and empirical relationships. Secondly, procedural knowledge specifies procedural relationships. Other authors, such as Rauch-Hindin (1988) and Deben-
ham (1989), also describe knowledge as relationship or association. Rich and Knight (1991) argue that knowledge serves two functions in AI programming. The first is essential knowledge that defines what can be done to solve a problem and what it means to have a problem solved. Secondly, heuristic knowledge states how best to go about solving a problem efficiently. Depending on the degree of accounting for principles and relationships, Parsaye and Chignell use levels of knowledge to distinguish shallow knowledge from deep knowledge. There are other characterizations of knowledge. McGraw and Harbison-Briggs (1989) state that knowledge can exist in many forms. They categorize knowledge into episodic, semantic, declarative, and procedural knowledge. Episodic knowledge describes long-term episodes or events, along with temporal-spatial relations among these events. Semantic knowledge reflects structure, organization and representation, and, like episodic knowledge, is long-term in nature. Abstraction is an important attribute of knowledge. Both Liebowitz and Lightfoot (1993), and Wiederhold include abstraction in characterizing knowledge. Wiederhold even extends abstraction to include generalization. 2.4. Declarative and Procedural Knowledge In sum, declarative and procedural knowledge seem to be the more common choices among authors. Description and relation, proposed by Hayes-Roth et al., belong to declarative knowledge. Fact and concept, proposed by Tuthill and Levy, is also part of declarative knowledge. Essential knowledge, proposed by Rich and Knight, is declarative knowledge as it describes what a system does. Essential knowledge of Rich and Knight, and definitional and categorical knowledge of Wiederhold, correspond in meaning to declarative knowledge proposed by Tuthill and Levy. Rule and causal knowledge, proposed by Wiederhold, is similar to procedural knowledge of Harmon and Sawyer. Algorithm and step, proposed by Lauriere, are part of procedural knowledge. Tuthill's definition on procedural knowledge specifies how things work, or "know-how," which is in some sense related to heuristic knowledge described by Rich and Knight. But, the former describes procedure as method and implies more than the best method (assisted with heuristics to reduce search space) as defined by the latter. It is regarded that heuristic is part of procedural
TABLE 2 Additional Characterization of Knowledge
Component (1)
Component(2)
Relationship
Function
Naming Describing Organizing Relating Constraining
Description Relationship Procedure
Declarativeknow. Essential know. Proceduralknow. Heuristicknow.
Level Shallow know. Deep knowledge
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Level of Details Domain / ControlKnowledge - KnowledgeContents Declarative/ Procedural Knowledge - KnowledgeFormats Fact, Concept,Relation/ Rule, Step, Algorithm,Strategy - DetailedKnowledgeItems
FIGURE 1. ParUculaflty. knowledge which includes method, step and procedures. Heuristic is to mean guidelines on how best to apply knowledge, using Rich's definition, although some other authors regard heuristic to be another type of knowledge by itself. It is often regarded mistakenly that domain knowledge is declarative and control knowledge is procedural. Van Harmelen (1991) has made an attempt to rectify this confusion. As argued by Van Harmelen, domain knowledge embodies contents of a problem domain whereas declarative knowledge is more concerned with the format written down. Domain knowledge can be written down in the format of either declarative or procedural knowledge. Likewise, control knowledge can also be written down in either declarative or procedural knowledge. In other words, both domain and control knowledge can be formulated as either one or both. For example, domain knowledge can be formulated, declaratively as logic, or procedurally as production rules. However, control knowledge can be either domain dependent or domain independent, but domain knowledge is usually domain dependent. 3. KNOWLEDGE ATTRIBUTES By consolidating all the different views presented in the previous sections, four knowledge attributes are identified. These four characteristics of knowledge, which constitute important ingredients for the multidimensional knowledge structure, are particularity, specificity, bipolaxity, and orthogonality. 3.1. Particularity
Particularity represents levels of detail. It is the quality of being particular and detailed. Generality and particularity form two extremes on a vertical continuum of multiple levels of detail. Lauriere's eight types of knowledge provide a useful classification framework for particularity. The three items of fact, concept, and relation can be grouped as detailed particulars of the declarative knowledge. The other four items (rule, step, algorithm, and strategy) belong to details of procedural knowledge (Figure 1). These descriptions of declarative and procedural knowledge are similar to proposals by Hayes-Roth
1
et al. (1983), Tuthill and Levy (1991), and Harmon and Sawyer (1990) as described in Section 2. Although both domain and declarative knowledge represent what a system knows, domain knowledge, as pointed out by Van Harmelen (1991), embodies contents of a problem domain whereas declarative knowledge is concerned with the format written down. Domain/control knowledge and declarative/procedural knowledge are assigned to two separate levels with different degree of particularity. 3.2. Specificity
Domain specific is a term frequently used in expert systems. Specificity is the depth of relationship with one particular problem domain. This quality can be described in terms of domain and control knowledge. Domain knowledge is dependent on and specific to a domain; control knowledge can be either domain dependent or domain independent. This implies that control knowledge is not specific to any one domain, though at the same time it does not apply to every domain. Thus, control knowledge is less specific, or has a lower degree of specificity, than domain knowledge. Conversely, we can also say that control knowledge has a wider scope of applicability, or a higher degree of generality, than domain knowledge (Figure 2). Specificity also applies to informed commonsense knowledge and commonsense knowledge, as described by Tuthill and Levy. Informed common sense has a higher degree of specificity than general commonsense knowledge as it is general knowledge specific to a particular environment. This pair of informed and general commonsense knowledge is more general than the pair of domain/control knowledge as the former is general knowledge. There are other cases that form pairs of generality versus specificity. Semantic memory knowledge is the organization of facts into hierarchy and is not connected to personal experience. This is a type of general knowledge. Episodic knowledge, on the other hand, is the selection from personal experience that belongs to a specific situation, and this is specific knowledge. In another case, deep knowledge (as described by Wiederhold, for example) is applicable to various situations and thus is general in nature. Whereas
Multidimensional Knowledge Structure
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Specific z ~x
Domain Knowledge - Domain-Specific Control Knowledge - Either Domain-Dependent or Domain-lndependent hfformed ComlnonsenseKnowledge - General, but Specific to a Particular Environemnt CommonsenseKnowledge - General
General FIGURE 2. Specificity.
shallow knowledge applies to a particular domain and so is specific, extensional knowledge is the set of all things denoted by a given concept. It generalizes concept and is general knowledge. Intensional knowledge determines what a specific concept means and is specific. All these are examples that form pairs of generality versus specificity.
3.3. Bipolarity Bipolarity represents two views of an entity. We make use of this dual-view quality to characterize knowledge into pairs (Figure 3). This is analogous to viewing the two sides of one coin. The pair of declarative and procedural knowledge is an example of bipolarity. On one side is know-what, as coined by Beerel, which constitutes fact, concept, and relation. The other side includes know-how, which comprises rule, step, algorithm, and strategy. Whether knowledge is declarative or procedural depends on viewpoint. This knowledge can be represented at the symbol level using logic or production rule. Domain and control knowledge are another pair that exhibits bipolarity. Domain knowledge is typically domain dependent whereas control knowledge can be either domain dependent or domain independent. These tw6 pairs are seen as equivalent to two poles on a horizontal axis, forming a bipolarity. These two views are coexisting and complementary, and not mutually exclusive of each other. Bipolarity implies that knowledge is interchangeable in format. The two attributes of specificity and particularity can also be regarded as bipolarity cases, as particularity and generality constitute two poles of an axis, this time a vertical axis. Likewise, the same applies to specificity versus generality.
3.4. Orthogonality There seems to be a paradox of "What versus How" with the two pairs of domain/control knowledge and declar-
ative/procedural knowledge. Both domain and declarative knowledge represent what a system knows, and both control and procedural knowledge are concerned with how a system uses what it knows. How can these two pairs be related together? And how can they be integrated and used together within a framework? As Van Harmelen has stated, domain/control knowledge differs from declarative/procedural knowledge in content versus format, and Davis (1993) indicates clues for the dilemma by saying "one person's floor is another person's ceiling." The paradox can be resolved by regarding these two pairs as orthogonal to each other. As shown in Figure 4, the two pairs can be arranged at right angles and are mutually perpendicular to each other, forming an orthogonality. This orthogonal arrangement indicates that contents of domain knowledge can be written in either declarative or procedural format. Fact, concept, and relation of declarative knowledge form part of the domain knowledge. Rule, step, algorithm, and strategy of procedural knowledge form the other part of domain knowledge. And the same applies to control knowledge. 4. A NEW K N O W L E D G E S T R U C T U R E The four knowledge attributes described in Section 3 serve as important components for the proposed multidimensional knowledge structure. It is multidimensional in nature because it assumes several measurements: hierarchical level and system view. Knowledge structure, as defined by Davis (1993), is a structured collection of concepts and their interrelationships. The two dimensions, derived from the four attributes, constitute the structured and related components of the structure. 4.1. Multilevel Structure The first dimension of the knowledge structure proposal is hierarchical in nature, forming a multilevel structure. Knowledge items are organized into levels and are related together through hierarchical relationships. The
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(a)
DomainKnowledge
ConWolKnowledge
Gen-Part substructure can be embedded into the Gen-Spec substructure. Thus, these two knowledge substructures are linked through an embedding relationship.
Venus
ProceduralKnowledge
DeclarativeKnowledge
~)
VS.
l)eCl~t~tl'~,e . rt~°~,l~tge
Gen-Part Substructure. Gen-Part knowledge substructure includes generality versus particularity. It describes knowledge contents by level of particularity, represented in a range descending from general to detail. Generality and particularity constitute two vertical bipolars in this knowledge structure. Figure 1 embodies the Gen-Part structure. Gen-Spec Substructure. Gen-Spec knowledge substructure includes generality versus specificity. Level of specificity is applied in this structure. The structure embodies knowledge, which ranges from general to domain-specific knowledge. Generality and specificity form another two vertical bipolars. Figure 2 embodies the Gen-Spec structure. 4.2. M u l t i v i e w Structure
VS.
The multiview knowledge structure adopts the multiple system views as the second dimension. It incorporates two knowledge attributes, bipolarity and orthogonality. Bipolarity allows a piece of knowledge to be seen from two sides. As described in Section 2, knowledge can be viewed either declaratively or procedurally. These two bipolar views constitute the basic structural unit in our
(c)
,.~
~
FIGURE 3. Bipolarity.
multilevel structure implies that there are multiple levels within the knowledge level. These multiple levels of abstraction are needed to consolidate complex domain details. Leveling helps to focus attention at issues appropriate to current level of abstraction within the knowledge level. It also assists to ignore complexity hidden at the lower symbol level. The multilevel structure incorporates two knowledge attributes, particularity and specificity, and is composed of two substructures, Gen-Part and Gen-Spec substructures. The
FIGURE 4. Orthogonality.
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Specific l~,arrow Domain
Principle
Far-Flung Domains BreadthHypothesis
FIGURE 5. Pyramid for narrow and far-flung domains.
knowledge structure. This knowledge structuring primitive, consisting of both declarative and procedural knowledge, is used as the basic building block for creating knowledge structure (Figure 3). Orthogonality allows multiples of bipolar views to be integrated, a sort of multiple of multiple views. As Van Harmelen points out, contents of domain and control knowledge can be formatted as declarative and/or procedural knowledge. A chunk of knowledge, composing domain and control knowledge, would also comprise declarative and procedural descriptions (Figure 4). This characteristic of knowledge is depicted as two pairs of bipolar views being arranged orthogonal to each other. Figures 3 and 4 together constitute the multiview structure. It should be noted that multiview structure also embodies the GenPart structure with different levels of abstraction as described in the previous section. In this sense, both multilevel and multiview structures are tightly integrated together.
4.3. Multidimensional Knowledge Structure From particularity to specificity and from bipolarity to orthogonality, the merging of multilevel and multiview structures gives rise to the multidimensional knowledge structure. Hierarchical levels and system views from the two dimensions. At the detailed knowledge items level, declarative knowledge can be broken down into particulars of fact, concept, and relation. Procedural knowledge comprises rule, step, algorithm, and strategy. At the knowledge format level, declarative and procedural knowledge together form two complementary views of knowledge. At the knowledge content level, domain and control knowledge can both be described with either declarative or procedural knowledge. It can
be seen from the structure that knowledge building is a continuous and recursive abstraction process, from lower level particularity to higher level generality and also from higher level specificity to lower level generality, and vice versa. This is in conformance with the interative, prototyping approach in ES development. All these knowledge descriptions are specific to a domain. Accumulation of multiple domain-specific knowledge contributes to the building of general knowledge. The wide base of the pyramid in Figure 5 represents this desired characteristic of generality. General common sense knowledge overcomes the brittleness shortcoming of the first era expert systems (Lenat, Prakesh, & Shepherd, 1986). This can, in the words of Feigenbaum (1992), "create a parachute for a soft fall by using more general knowledge of a nonspecialist sort to do some kind of problem solving when the detailed expert knowledge is lacking." It should be noted that general knowledge also incorporates the basic knowledge structuring unit that is described in multiview knowledge (Figure 6). In sum, what we have produced is a spatial organization of knowledge. This static structure describes the positional relationships among different facets of knowledge.
4.4. Comparison to Other Knowledge Structures Many authors have incorporated multiple levels of abstraction in classifying problems. Examples include Clancey's heuristic classification on problem solving (1985) and Chandrasekaran's hierarchical classification on generic tasks (1986). We classify knowledge not just by level, but also by view. This constitutes the most important difference between our work and others. Shaw and Woodward (1990) describe three dimensions of
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knowledge, view, knowledge type, and level. These three dimensions together share some similarities to our multilevel and multiview proposal. Yeh and Zave (1980) identify three structuring primitives, namely partitioning, abstraction, and projection. Partitioning and abstraction capture the structural relations of aggregation and generalization, respectively. Projection corresponds to a view of the structural relation. Projection is similar to the bipolar and orthogonal views we previously describe. However, our system view is derived from bipolarity, whereas orthogonality allows for multiple dual views. In a sense, multidimensional analysis in knowledge acquisition shares some similarities with the knowledge structure in terms of its dimensions. The card sort technique, which belongs to multidimensional analysis, uses factor (overall scale) and level (card piles) as the two dimensions. Level is similar to our multilevel structure, but factor is not. Our research concurs with Rauch-Hindin that structure is present in knowledge. However, we differ from the knowledge structuring primitives that Brachman (1979) has proposed at the epistemological level. The KADS approach views knowledge modeling as the major challenge. We regard that characterization of knowledge contents is a high priority item. 5. TIMETABLING APPLICATION This section describes a timetabling expert system (Martinson, Kwan, Chow, & Lo, 1993) that is applied with the knowledge attributes and structures presented in Sections 3 and 4. Academic timetabling, as a kind of scheduling, is one of the more important and complex administrative activities in formal education. In larger institutions, such activities are often consolidated and
assigned to a group of individuals, the schedulers. Timetabling represents the allocation of scarce time and room resources for study programmes subject to the constraints and preferences of teachers and students. The traditional method for creating academic timetables is through the manual approach, which is time consuming and tedious. Such characteristics would make this domain an ideal candidate for computerization. A variety of computerization approaches have been attempted. This includes simulated manual processing, graph theory, optimization, etc. However, the complexity of programmes and resources, together with the constraints imposed, make satisfactory solutions difficult. A knowledge-based approach provides a new dimension to tackle the timetabling problem. In the academic environment, for which the Timetabling Expert System is developed, scarcity of time is of particular concern for the part-time evening study programme. Part-time students are required to come for lessons on only three evenings per week with a normal load of two to three subjects. However, there are only three teaching hours in each evening. There is a need to schedule classes in all the available teaching timeslots on those three evenings. This constitutes the tightest constraint from the student side. The schedulers' knowledge to get around this constraint of scarcity in timetable timeslots is modeled. These many facets of knowledge related to the constraint are organized into domain/ control knowledge, declarative/procedural knowledge, and detailed knowledge items, as sampled in Table 3. The two pairs of domain/control knowledge and declarative/procedural knowledge form two separate bipolars and represent different ways of viewing timeslot scarcity constraint at both content and format levels. These two are broken down into detailed knowledge items, such as
Narrow Domain
Far-Flung Domains
FIGURE 6. Multidimensional knowledge structure.
Multidimensional Knowledge Structure
185 TABLE 3 Sample Tlmetabllng Knowledge
Knowledge content • Domain knowledge Constraint on timeslot scarcity (Specific to timetabling domain) • Control Knowledge "lqmeslot selection (Timetabling dependent) Forward chaining, backward search (Timetabling independent) Knowledge format • Declarative Knowledge Fixed number of timeslots in timetable • Procedural knowledge Timeslot selection policy Timeslot priority scheme as constraint satisfaction strategy Updating of selected timeslots to student data base Detailed knowledge items • Fact: Timeslot, timetable, priority value, student (class) • Concept: Choosing a suitable timeslot • Relation: Positional relations between different timeslots
• Rule: lqmeslot selection rules, conflict relief rules • Step: Sequence of timeslot (& room) selection followed by conflict relief • Algorithm: Update selected timeslot to student data base file • Strategy: Scheme to assign priority value to timeslots in student's timetable
timeslot, conflict relief rule, priority scheme, etc. The three levels are arranged in a knowledge hierarchy, the Gen-Part structure, representing different degree of particularity. The two pairs of bipolars form orthogonality as shown in Figures 3a-c. They also become the multiview knowledge structure. Domain-specific knowledge is essential in being the source of power for solution. However, this domain specificity also creates the brittleness problem. For example, the timetabling expert system is not prepared to handle other constraints such as balancing the interests of different groups, staff, students, etc., so that one is ill-treated in the midst of scheduling conflicts. Automated arbitration knowledge, belonging to another domain, seems far away to be readily helpful. 6. DISCUSSION & CONCLUSION The proposed knowledge structure to characterize the contents of knowledge is specific to Knowledge Level. This section attempts to relate the proposed structure to the lower levels within Newell's 4-level framework, with particular emphasis on the symbol level. Multiplicity in AI/ES is now new. Bobrow (1986) has argued for an adoption of multiple programming paradigms for AI programming. Multiple knowledge representation is not new either. Sloman (1985) proposes that there exists a need for various knowledge representation formalisms and advocates the use of many (or multiple) knowledge representations. Mixed representation formalisms have been used to represent different types of knowledge. For
example, KRYPTON (Brachman, Fikes, & Levesque, 1983) represents definitional and assertional knowledge; KLTWO (Vilan, 1985) uses two different languages to deal with propositional and quantificational reasoning; and KEDE (Zheng & Li 1992) handles as many as five kinds, in addition to mixed reasoning mechanisms. As put forward by Reichgelt (1991), one of the questions to follow this multiple representation argument is when to use which knowledge representations. In an empirical study of knowledge elicitation techniques, Burton, Shadbolt, Hedgecock, and Rugg (1987) conclude that the order of using knowledge elicitation techniques does not make any difference in the quality of knowledge elicited. This clue indicates that the order of establishing declarative and procedural knowledge is not important in creating the primitive knowledge structure. We suggest not to prescribe any procedural sequences in deriving declarative and procedural knowledge, as well as in domain and control knowledge. Gammack and Young (1985) have argued that different knowledge types should be matched to appropriate knowledge acquisition techniques. Like knowledge representation, combined use of knowledge acquisition techniques can be adopted to elicit both declarative and procedural knowledge. As described by McGraw and Harbison-Briggs (1989), interviews are good for eliciting declarative knowledge. Card sort can also be used. Structured interviews, process tracing, simulation, and protocol analysis help in elicitation of procedural knowledge. Laddered grid is a useful technique to develop a hierarchy of knowledge. However, McGraw
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and Seale (1987) caution that use o f these techniques should also be related to development phases. This points to our further work. Expert system as an end-product is a moving target. The proposed knowledge structure better accommodates changes. This is achieved by structuring of knowledge which in turn structures the ES development process. Although this paper emphasizes the need for a knowledge structure, overemphasis on structure results in rigidity. Flexibility in the ES development process should be accounted for balancing against rigidity. Multiplicity allows for built-in flexibility, as extension with more levels and more views is possible. Furthermore, dimensionality can also be incremented. Other possible dimensions include temporal and control. Through this multidimensional framework, flexibility and extensibility enhance ES development. A structure is an important prerequisite for any attempt to scale up expert systems. Knowledge sharing, very large knowledge bases, and large-scale interoperable expert systems are emerging as important research areas. Some pioneering projects include CYC (Guha & Lenat, 1991), for building large-scale general common sense knowledge, and PACT (Cutkosky et al., 1993), for demonstrating the feasibility o f distributed, interoperable knowledge systems. A Knowledge Interface Format (KIF) has been defined for knowledge sharing. More work is needed to explore their relationships to the knowledge structure. Other work includes defining a framework for mapping knowledge attributes and structures to knowledge representation method and knowledge acquisition techniques. Even with the several view shifts already undergone in AI/ES, knowledge is still occupying a central role in ES development. In characterizing knowledge contents within the context of Newell's knowledge level, particularity, specificity, bipolarity, and orthogonality are identified as knowledge attributes. Based on these, a multidimensional knowledge structure composed of multiple levels and multiple views is proposed. As knowledge is the primary source o f competence, structuring knowledge becomes an important prerequisite for any attempts on AI/ES solutions. The major contribution of this static spatial structure is that it describes the positional relationships among different facets of knowledge and gives clarification on the characteristic of knowledge.
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