Predictive models of information systems

03oMs73/xI/020103_09$11?.w/0 Pergamon Presr l.ld

PREDICTIVE MODELS OF INFORMATION SYSTEMS PRANASZUNDE School of Information and Computer Science, Georgia Institute of Technology, Atlanta, GA 30332,U.S.A. (Received for publication 8 /u/y 1980)

Abstract-The problem of modelling information systems is studied with focus on predictability. Predictability presupposes discovery and knowledge of empirical laws and theories, which are in the domain of information science. Discovery of such laws and theories goes hand in hand with the development of the capability to measure important variables in that domain. The state-of-the-art of predictive modelling is discussed with respect to syntactic, semantic, and pragmatic criteria, emphasizing the need for concentrated effort in further development of the empirical foundation of information science.

INTRODUCTION

science studies the nature of information as it manifests itself in phenomena related to information generation, transmission, transformation, accumulation and storage. Since these are directly or indirectly observable empirical phenomena, information science is an empirical science, in contrast to a priori sciences, such as logic or mathematics, which start from postulates assumed to be true and proceed to demonstrate what consequences can be derived from these postulates. The principal objective of an empirical science, other than the description of empirical phenomena, is to establish general principles by means of which empirical phenomena can be explained, accounted for, and predicted. The explanatory and predictive principles of a scientific discipline are stated in its hypothetical generalizations, its laws and its theories: they characterize general patterns or regularities to which the individual phenomena conform and by virtue of which their occurrence can be systematically anticipated [I]. In engineering terms, empirical laws and theories can be called models of natural phenomena. Applied to technological problems, empirical laws provide the necessary tools for solving these problems, such as designing all kinds of systems. In particular, empirical laws enable a system designer or engineer to construct in the initial design phase mathematical models of the system and then use such models for the purpose of testing and evaluation with more or less the same effectiveness as testing and evaluating the system itself. This is what, for instance, an electrical engineer does when he applies Kirchoff’s, Ohm’s and other laws of physics to the design of electrical circuits. One would then expect information science to contribute to the advancement of information engineering what physics did to the development of mechanical, electrical, nuclear and other engineering branches. And it eventually will. At this time, however, the process of discovery of empirical laws and general principles of information science is in its early stage and systematic work on validating such laws and constructing theories has hardly begun. This paper discusses fundamental concepts of empirical foundations underlying information systems design and modelling, explicates the semiotic dimensions underlying such models, and investigates the prerequisites for developing predictive models of information systems. Information

SYSTEM MODELING

Short of its implementation, the design of an information system, like that of any other system, essentially reduces to identifying a set of system alternatives which are feasible with 103

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respect to existing financial, technological, and other constraints, evaluating these alternative\ relative to system objectives, and then selecting as design solution an alternative which is optimal. In traditional engineering fields, such as mechanical or electrical engineering, whenever a designer (i.e. an engineer) is faced with a set of alternatives. the common approach ih to construct a model of the piece of hardware or system and use the model to evaluate available alternatives for optimal solution. The system which is being modeled may already exist and the model may be used to upgrade or modify the existing system; or it may not exist. in which cahe modeling is part of the process of the design of a new system. Roughly speaking, a model is some kind of entity (physical replica, computer program, mathematical equation, etc.) which portrays, reproduces or simulate{ certain aspects of the system under consideration. The crucial thing in the construction of a model is to find an optimal trade-off between the simplicity of the model and its capability to satisfactorily represent the aspects of the system which are modeled. On the one hand, it seems intuitively plausible that a model which resembles the system in greater detail is more likely to better serve the purpose of the designer than a simpler model of that system. One would thus argue that, all other things being equal, complexity of a model should be regarded as one of the indicators of its goodness. But then one would be led to the conclusion that the best model is an exact replica of the system itself. That clearly defeats the other purpose of modeling, i.e. to construct a sufficiently good “surrogate” of the system at relatively low “cost.” From this point of view. models should be as simple as possible. And so we have two opposite tendencies-complexity vs cost (in a general sense) which need to be traded off in some optimal fashion in choosing ;I model for a particular system. The way of achieving such a trade-off is to select for modeling only such characteristics or aspects of the system as are relevant and sufficiently significant with respect to the objective of modeling. For example, if one is constructing a model of a communication system for the purpose of optimizing the rate of message flow, some of the important features of the system are channel capacities. distribution of messages in time, distribution of messages by length and structure of the network, whereas features such as contents of messages. salaries of the operators, and color of terminals are not significant features. Similar criteria need to be applied also to the selection of significant relations among the variables of the system. which are to be reflected by the model. It follows as a consequence of the preceding remarks, amply supported by practical experience of model designers, that, on the one hand, the same system can usually be modeled by different types of models and. on the other hand, the same type of model can be used to model a variety of systems. Although a single classification of various types of models is difficult to come by because of the comprehensiveness and. on a deeper analysis. apparent ambiguity of the concept of the “model” in its various uses, partial classifications can be made on selected bases. For modeling information systems, the most important types of models are the ones derived, firstly, on the basis of the function served by a model and, secondly, on the basis of physical nature of the model. On the basis of the function served, models can be classified into descriptive, predictive and normative; on the basis of their physical nature. into iconic, analog and abstract. The main purpose of a descriptive model is to portray how the system looks in {ome respect of interest or what it does. A flow diagram, an organizational chart or a facility layout diagram is an example of a descriptive model. A model is called predictive if one can use it to determine system behavior in response to external inputs or changes within the system. or. more generally, the effect of changes of some set of system variables on others. Examples of this kind are models of information scatter. Finally, normative models are intended primarily as tools in selecting a course of action in the face of several alternatives; such. for instance, are models of library stock management. As to the second classification, a scaled 3-dimensional replica of an airplane used for testing experiments in a wind tunnel is an iconic model. In cases where one property or component is used to represent another property or component of what is being modeled. the model is known as an analog model. Analog and digital computer simulation models provide an example for this category. Finally, abstract models are the ones which are constructed of symbols: natural

105

Predictive models of information systems

language texts, diagrams, drawings, etc. A particularly important subcategory of this type are models in which the symbols employed represent quantities. They are usually called mathematical models. For example, in Ohm’s Law, E = IR, the symbols E, I and R are used to represent voltage, current and resistance expressed in appropriate units, In this article, we will be primarily discussing abstract predictive models. SEMIOTIC

DIMENSIONS OF INFORMATION SYSTEM MODELS

What is it peculiar about information systems that needs to be considered in modeling? It is the nature of what is being processed by them, i.e. the nature of information itself. Man-made information systems are primarily intended to process information conveyed by sign events. An event is a sign event or semiosis if and only if it involves something which acts as a sign (S), something which the sign refers to (O), and somebody to whom the thing in question is a sign (1)[2]. The latter is called an interpreter. Thus, a sign event can be visualized as a ternary relation on a set of objects such that for some three objects 0, S and Z, S is a sign of 0 for an interpreter I. The diagram of this relation is shown in Fig. I. Often sign events are not just occurrences of unrelated individual signs, such as smoke being a sign of fire to some observer (interpreter) or train whistle being a sign of train departure. Rather, they are ordered sequences of signs in some (natural or artificial) sign systems. Examples of the latter are messages communicated by smoke signals, utterances in some natural language such as English, and computer programs. An ordered sequence of elementary signs (such as words) in some sign system (language). in an overall semiotic context (such as a book, an utterance or a sequence of smoke signalsj-not excluding a trivial sequence consisting of a single sign-is called a text. In the sense of communication, texts may be viewed as tools for conveying messages, which contain potential information to a “receiver.” Information contained in a particular message may differ in some quantitative sense from one receiver to another. Thus a message contains no information (“zero amount” of information) if the receiver (interpreter) cannot comprehend it or if he is already familiar with the contents of the message, or a lot of information if it makes a receiver less uncertain about possible outcomes of events of great interest to him. Man-made information systems can be viewed, in a broad sense, as text processing systems intended to satisfy in some optimal fashion information needs of their users. Because of the inherent complexity of sign processes it is often convenient, in analyzing them, to simplify the analysis by limiting it to certain semiotic levels or dimensions. The most common notions of such semiotic abstractions are associated with the syntactic, semantic and pragmatic dimensions of sign processes[Z]. Analysis of a sign process is on the syntactic level if the concern is limited to the formal rules of sign formations and sign transformations; it is on the semantic level if the concern of analysis is focused on the relationship between signs and what they stand for, i.e. on the aspects of meaning; finally, the analysis is on the pragmatic level if the interest is focused on all kinds of effects of sign processes on interpreters, such as the effects on their behavior, value judgment, social attitudes and morals and esthetics. But it is important to keep always in mind that these levels are just for the convenience of analysis and that every actual sign process always encompasses all the three dimensions.

Fig. 1. Sign event as a ternary relation: S-sign, O-object, of which S is a sign, I-interpreter, is a sign of 0.

to whom S

P. ZCNDF

106

The above concepts of semiotic dimensions extend in a natural way to information associated with texts and as such, prove to be very fruitful in modeling information systems both for analysis and design purposes. Thus, everything which is lost in the sense of information by abstracting, in information processes, from user’s (receivers, interpreters) behavior. attitudes, reactions, etc. constitutes the pragmatic dimension of information. Next, everything which is lost in abstracting from the information related to the meaning of texts, constitutes the semantic dimension of information. What remains is the syntactic dimension of information. In particular, analysis on the syntactic level of information deals with the effect of formal text structure on its information contents. We shall return to application of this kind of semiotic analysis to modeling of information systems in one of the following sections. PREDICTABILITY

One of the main uses of models is to predict the behavior of the system or to predict systems outputs in response to certain inputs to or internal changes in the system. Although descriptive and normative models have reached a high level of sophistication in their latest phase of development, predictive models should nevertheless be viewed as superior in the sense that the builder of these models has to go beyond descriptive representation of the characteristics of the system being modelled and has to incorporate in these models laws of nature which give them the capability to predict. To clarify this point, let us turn again to an example from traditional engineering. Assume that the system to be designed is the electrical network shown in Fig. 2. It consists of an electrical voltage source (i.e. a generator) an inductor with inductance equal to L henries, a capacitor with capacitance of C farads and a resistor of R ohms. Let i(t) denote the current in the network. Assume the current i(t) to be the input (i.e. something which can be manipulated) and the voltage e(t) to be the output of the system (i.e. that particular variable which we want to observe in its dependence on inputs). The mathematical model, which we are about to design should enable us to reliably predict the outputs, namely the voltage in the system, from the inputs, namely the current which we are free to manipulate at will. In constructing a mathematical model of this system, we first note that in physics there are available empirical laws which relate voltage and current for each of the components of the system in Fig. 3,. Thus the voltage drop tlK across the resistor is given by the Ohm’s law vK = Ri. The voltage drop cl. across the inductor is given by the Farraday’s di t’I = 1, z = LDi

(1) law

(2)

and the voltage drop tic- across the capacitor is given by the law

L’(.

=

I (’

-

I,,‘I +9 =+D dt

Fig. 2. Series RLC Circuit

(3)

Predictive models of information systems

and

IO?

by dx 1 Dx(t) =-gcZrx(t)=

The above three laws can be linked together by the Kirchhoff’s Law or principle, which states that in any closed circuit the sum of the voltage rises must equal the sum of the voltage drops: i.e. UL +

UR t

UC =

e(t).

(4)

Substituting for UK,nLand uCin eqn (4) the expressions from (1) to (3), we immediately obtain the required mathematical model for the systems in Fig. 2 in the form LDitt)t R(t)

+a

1

i(f)

= e(f)

(5)

which establishes the functional relationship between the input i(t) and the output e(t) and permits us, for any given value of the current i(t), to determine or “predict” the unique value of the required voltage e(f). If. instead of the current i(t), we would have chosen, say, the voltage drop ORacross the resistor as the input, we could have constructed by a similar procedure a different model establishing the relationship between uR(f) as input and e(t) as output of that system 131. It should be clear from this simple example that the capability to construct models which could be used to predict systems behavior depends, first of all, on the availabiIity of appropriate empirical laws to the designer and secondly, on the richness of the conceptual fabric of such laws and theories reflecting various dependencies between variables and parameters of the system which is to be designed. This, of course, is in turn a reflection on the state of development of relevant branches of science. Physics and chemistry are characteristic examples of best developed empirical sciences, and thus a designer of mechanical, electrical, nuclear and other systems which process matter and/or energy, has a well stocked bag of reliable tools to build predictive models. It is not at all necessary that empirical laws underlying such models be all deterministic, as are those in our preceding example. In fact, stochastic empirical laws are often more “realistic” and in well developed branches of science, are completely compatible with deterministic laws, as demonstrated by well known examples of traditional and statistical thermodynamics and mechanics. Empirical sciences which study information and information processes are much less developed than physics or chemistry and our knowledge of laws of sufficient generality involving information reiated phenomena is, at this time, rather limited, even though significant contributions in this direction have been lately made by a number of scientists [4,.5]. MODELING

INFORMATION

SYSTEMS

Let us now pose, in the form of a general paradigm, a hypothetical information system design problem. This system S is to process texts containing information (texts are to be interpreted in the broad sense discussed earlier in this paper) and is to be viewed as an input-output system. Then, by analogy with traditional engineering practice, the essential problem of the design is to construct a model of the information system which would relate, in some specified fashion, information contained in the input u(t) to information contained in the output y(t) of the system and would satisfy certain optimality requirements (such as relevance, cost, value to the user, etc.) embodied in some specified performance or criterion function J (Fig. 3). This is to be a predictive model, i.e. it should be possible, by using this model, to explain, account for, and predict input-output behavior of the information system and evaluate design alternatives. The question is to what extent it is possible to construct such a model. We have already noted that modeling of information systems involves considerations of syntactics, semantics and pragmatics. Depending on the type of the information system, one of those semiotic dimensions may be the dominant design factor. Analysis of such types of

I ox

P. ZLIHDE

u(t)

_

Input Text

(Information)

Output b

Fig. 3. I/O Information

Text = y(t)

S;J (Information)

System 5’. with Performance

l

Junction J.

can be indicative of our capability to approach the ideal of predictive modeling. Here are some examples. A case of an information system design problem which is primarily of syntactic nature is modeling a communication system. It takes texts containing messages as inputs u(t) and produces same as outputs y(f). A designer of a communication system, a communication engineer, is not concerned with the meaning of inputs or outputs (messages), or their values, effects, etc. to or on receivers. He is only concerned with formal properties of various transformations of the shapes of signs which are being transmitted, subject to certain optimality criteria. which are essentially syntactic in nature. too. In other words his concerns are that characters or sounds or groups of characters or sounds of input texts be converted (encoded) into sequences of, say, pulses and that there would be an invertible one-to-one correspondence between these two sequences; that the system would be sufficiently powerful to transmit pulses of electric current or electromagnetic waves a required distance in space through an appropriate medium; that the text be recovered with the fewest possible errors from the signals received at the destination and the like. The objective function J,? of this kind of a system may, for instance, be to minimize the error rate in transmitting texts by appropriate encoding methods, to use the available communication channels to their maximal capacity. or to operate the communication system with minimal costs. Hence, in this kind of a system variables of main interest to the designer are those related to physical properties of sign vehicles or carriers, which always are physical objects, or events involving physical objects. Empirical laws reflecting all kinds of relationships among these properties are the laws or physics, chemistry, biology and related sciences, which as we have already noted, have a well developed theoretical structure. The results of these branches of science, together with certain formal theories specific to the communication field (coding theories, etc.) make it possible to construct, in most instances, good predictive models of communication systems. Next, let us take an example of an information system design problem which is primarily of semantic nature: a system which automatically translates from one natural language into some other. This system receives as inputs I texts in language L,, say English. and translates these texts into language L, say German, translated texts being the outputs y(t). The objective function JM would be some criterion which reflects the degree of discrepancy (or, conversely, the degree of correspondence) in meaning between a text in language L, and the translation of that text in language L2. Still, the designer would not be concerned with the value of those texts to the user so that pragmatic considerations would not play an essential role. Other examples of this kind of design problem are automatic abstracting and scene analysis. To model, in a predictive mode, various relationships between inputs and outputs of this kind of a system and to evaluate the outputs, empirical laws relating meanings of words (or, more general, meanings of signs of any kind) in the two languages (or sign systems) as well as laws relating meanings to other observable phenomena. such as sentence structure, frequency of occurrence of words, etc. are required. Beyond that, systematized knowledge is needed linking empirical laws and other observed regularities into unifying semantic theories (i.e. theories of meaning). Some such laws have been proposed, although their status is, at this point in time, mostly hypothetical. Examples of hypothetical laws of this kind are: 0 The more frequently a word is used, the more meanings it tends to have, the relationship being fi = c,\‘F. where FI is the average number of meanings of all words of frequency F and c, is a parameter depending on the length of the text [6]. 0 The greater the length of the word, the fewer meanings it tends to have[7]. systems

Predictive models of information systems

109

l A subject gets more conditioned to the meaning of a word than to its mere visuafauditory form [Q l Word pairs which are associatively most similar to one another are also judged to represent the most similar concepts [9]. Lately, interest in laws involving semantic variables has been greatly stimulated by work on question answering information systems, dialog systems, “intelligent” information retrieval systems and the like, but as yet results are few and of marginal significance and more comprehensive theories of semantic phenomena have not been developed at all. Until then our capability to construct predictive models of systems involving semantic variables will be quite limited, Finally, let us consider as an example of a design problem which emphasizes pragmatic considerations: modeling of a management information system, Inputs u(t) into such a system are queries or requests for information required for various management decisions and outputs y(t) are texts, retrieved or computed, containing information; the objective of the system is to maximize the value of output information to the management and the degree to which, this objective is achieved is monitored by the objective function Jp. In this example, the dominating issue is the value of information delivered by the system to its user-a distinctly pragmatic characteristic. Predicting system performance in terms of value as output variable requires empirical laws relating information value to users’ goals and other variables and to system parameters such as selectivity, processing lag, volume of stored and/or accessible information, etc. At present we have only a few conjectures regarding the dependency of information value on other variables, such as the conjecture that information value declines with time according to negative exponential law. Equally scanty is our knowledge of empirical laws invoiving other characteristically pragmatic variables such as relevance, comprehension, intelligibility, responsiveness or timeliness. generalizing from the above examples and assessing our overall capability to construct predictive models of information systems, one would have to conclude that it is essentially limited to syntactic variables of the system. When the system is to be modeled primarily in terms of syntactic variables, such as information transmission systems, it is possible to construct models which can be used to predict and evaluate the behavior of the system to a high degree of accuracy. When, on the other hand, the model is to emphasize semantic and pragmatic aspects of the system, the possibilities of constructing a predictive model of sufftcient reliability are at present very limited. The reason for that is our limited knowledge of empirical laws and theories underlying informational phenomena. It will surely advance with the advancement of information science as an empirical discipline. MEASURABILITY

There is also another important issue associated with modeling information systems in terms of semantic and pragmatic variables, which needs to be explicitly stated. It has been claimed that science begins with measurement. And even though this claim may be exaggerated, there is no doubt that advances in science and advances in theory and technology of measurement are highly interdependent and mutualIy stimulating. In particuIar, discovery of scientific laws and theories in their abstract mathematical form, which, as we have already seen, constitute the backbone of predictive models, presupposes the capability to measure quantitative properties which occur as variables in such laws. For example, Ohm’s law in its well known mathematical form could not have been discovered if there had not existed the capabilities to measure electrical current, voltage and resistance. Unfortunately, our capability to measure information in its various forms and manifestations as well as our capabiiity to measure other variables important to information studies is considerably behind the capabilities of a physicist, a chemist or a hardware engineer to measure variables with which they are primarily concerned. Except for measurements of the medium or the physical carrier of information, such as signal propagation velocity, wave amplitude, or channel capacity, which actually have been developed in the physical sciences, most other aspects of measurement, in particular measurements of semantic information and measurements of pragmatic information are not at all well developed[l~]. The inability to measure effectively important variables of semantic and pragmatic nature has a negative effect

P. %LlWF

I IO

only on the design but on modelling limits significantly our capability to implement efficient system design for the following reason.

optimization

Llsually there are a number of available alternative solution\ design procedure should provide for, and if possible. incorporate mechanism for selecting a solution

which would be “best”

systems in procedures

It in the

to a system design problem: a into the model of the system a

or optimal

in some specified manner.

This optimality criterion is formulated as ;I performance function J. which has been already discussed in the preceding section. This function ik rel:lted to the important parameter or parameter\ of the mathematical model of the system. For instance. if these parameter\ are input\ and state4 of the system, then the value J( II. .Y) i\ a mea>urt’ of how ~rll particular inputs u and states .x cause the system to perform

with respect to bpecitied

criteria.

criteria of performance, often applied in practice. arc coht of processing, perform an activity. optimal utilization of certain resources and error rate.

Example:,

of

time required

to

In the design of an information system, effective performance criteria, such as minimal cost. are usually functions of selected important variable>. such as quality of information, retrieval prcci\ion or query relevance. clearly, such performance criteria uill he reliable only to the extent that the variables appearing in it are satisfactorily measurable. For ;I simple example, if the performance top value relative

criteria

for an information

system is to deliver

to the needs of the users at minimal

highly selective

co\t, this criterion

information

of

LWII~ he effectivei)

applied in modeling for design optimization if and only if there were dell developed procedures and method\ to measure information value. Hut. ax we have jeen. this variable as well ;I$ most of the others which naturally

would appear in performance

we at present cannot satisfactorily

criteria

are cuxtly

the ones which

measure.

SlJMMARL

AND

C’ONCLUSIONS

In many instances a system designer’s ideal is to be able to construct a predictive model of the system and use the model to evaluate detign alternatives in terms of predicted behavior of the system.

For mechanical.

electrical.

chemical

and other

traditionA

engineering

designs,

which have their roots in well developed sciences \uch as physic\ and chemistry. construction of predictive models is a feasible undertaking. Not so in design area\ which have to rely on not w well developed sciences, such as design of information systems. Predictive modeling of systems is based on empirical laws and theories. i\ the goal of every empirical

science. Discovery

of empirical

discovery

Iii\ j ,~nd development

of which of theories

goes hand in hand with the development of the capability to adequately measure important ~nriahles. Information science is a relatively young science and although impressive progress ha\ heen made in developing its foundations. more general law\ :!nd theories relating broad categories of information need yet to be discovered. Further advance\ need ;tljo to be made in measurement

of such essential quantities

as information

value. utility.

relevance.

timeliness

and

oh5olescence. The present state-of-the-art of predictive modeling of information systems naturally reflects the state of information science as an empirical discipline. If \,ariable\ of main interest to system design are variables

associated

with physical

carriers of information

for which laws of

physics and chemistry hold. then predictive modeling is possible hith a high degree of success (such a\ modeling communication systems). On the other hand, if the main interest of the \ystem’s designer is in variables of a semantic and pragmatic nature, the possibilities of predictive modeling of such systems are at present limited. Readers interested in further details on the development of empirical foundations of information \cience and the impact on information system design are referred to Ref\. [ 11. 31.

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