# Logic and Meaning in Conceptual Models: Implications for Information System Design

Publishing History: This paper was first published as Warwick Business School Research Paper No 62. University of Warwick, Coventry CV4 7AL, United Kingdom, May 31, 1992. It was reprinted, with the addition of a preface, in Systemist Vol. 15 (1), Feb 1993.
Note on Figures. Figures 1 and 4 have been abstracted from the the figures that appeared in the original publication. This is to avoid any possibility of international copyright infringement.

### Abstract

A number of logical problems in conceptual modelling can be solved by expressing the models in the form of universal statements. This leads to distinguishing two type of conceptual model, those used in main stream SSM and those used in Multiview, on the basis of whether the universals are definitions or inductive hypotheses. The models can be formulated in the predicate calculus and these formulations can be converted into the rules of Knowledge Based Systems.

### Introduction

There is an ongoing debate about how Conceptual Models can be used in the process of information systems analysis and design (see Mingers 1992). Much of this debate can be characterized by its extreme generality. It has not been accompanied by a detailed analysis of Wilson's Information Requirements Analysis (1984, 1990) or Avison & Wood-Harper's Multiview (1990). Both methods use Conceptual Models in information system design, and the proponents of both claim that these methods are well tried in practice.
In a separate development Probert (1990) has challenged the fundamental basis of Conceptual Modelling. Wilson (1990) and Checkland & Scholes (1990) claim that their Conceptual Models show logical dependencies. Probert argues that their models cannot be logical in any sense of the word. This argument can is answered in the first section of the paper which also reveals two important facts about Conceptual Models. The first fact is that the Conceptual Models produced by Wilson and Checkland in their Soft Systems Methodology (SSM) are "logical" in a quite different way from the way in which the Multiview models are "logical". The second fact is that an analysis of SSM Conceptual Models reveals hidden premises. The elements in the models can be understood as corresponding to particular statements. The hidden premises correspond to universal statements. In the predicate calculus Conceptual Models can be expressed entirely in universal form.
The universal/particular distinction has implications for information system design. The rules for Knowledge Based Systems can derived directly from universals. The argument, therefore, turns full circle. Objections to the logic of Conceptual Models prompts a deeper analysis, the deeper analysis shows how the models can reveal a logical structure suitable for information system design.
In spite of this, there are ambiguities about the status of SSM models. This is brought out in the second section of the paper which considers the origins of universals. Three types of universal are identified: inductive hypotheses, value statements and definitions. It is argued that the SSM models are definitional. This creates problems in determining that a given model has any relation to the real world because this would seem to involve an inductive hypothesis.
Multiview models, by contrast, are collections of inductive hypotheses. The third section argues that Multiview is faced with a problem that is the opposite of SSM: a hypothesis can only be formulated in a language, a language requires definitions and the Multiview model building does not generate definitions.
The paper concludes by suggesting that a new type of model could be constructed. The new models would include definitions and inductive hypotheses thereby combining the advantages of the SSM method with those of Multiview. A further feature could be the inclusion of value statements. This would make the models logically comprehensive as well as adding a new dimension to the model building process.

### The "Universal" Solution
#### The logical problem

The word "logic" has come to mean a variety of things. The Collins English Dictionary gives seven definitions, only two of these will be relevant here: 1. the branch of philosophy concerned with analyzing the patterns of reasoning by which a conclusion is drawn from a set of premises, without reference to meaning or context. ... 6. the relationship and interdependency of a series of events, facts etc.
The conceptual models in SSM are represented as words contained in bubbles which are joined by arrows. The arrows are intended to show a relationships of "logical contingency". Thus in figure 1 a bubble containing the words "Discharge patient" is connected by an arrow to another bubble containing the words "Apply treatment". A vital point here is that this could function on one of, at least, two levels. The arrows could be intended to show logical contingency between the expressions in the bubbles (first level) or logical contingency between real world events that correspond to these expressions (second level).
If the logical contingency is intended to be at the second level then this will be consistent with the definition of logic in sense 6. This is exactly what "logic" means in the Multiview Conceptual Models: "use arrows to join the activities that are logically connected to each other by information, energy, material or other dependency..." (Avison & Wood-Harper, p.60).
This is quite different from the account of Conceptual Models given by Wilson and Checkland. They make it quite clear that their models are not intended to be models of real states of affairs.
"It cannot be emphasized too strongly that what the analyst is doing, in developing a HAS [Human Activity System conceptual] model, is not trying to describe what exists but is modeling a view of what exists." (Wilson 1984).
In an earlier paper (Gregory 1992a) a distinction was made between a model that is conceptual and a model of a concept. It was argued that SSM models are models of concepts and, therefore, the logical contingency should be understood as being at the first level. This interpretation not only fits well with main stream writing but also allows us to describe the models as being "logical" in sense 1. This in turn allows the models to be expressed in standard symbolic logic which is useful in relation to information system design (Gregory 1991, 1992b, Merali 1992). Therefore, provisionally at least, we can take it that the SSM models are not logical in sense 6. and that the Multiview Conceptual Models are a different type of thing.
Probert's argues that the arrows in the SSM models cannot be logical in sense 1. because the contents of the bubbles are imperatives, and logical relationships in sense 1. can only hold between declaratives. "Discharge patient" is a command and standard logics only operate on statements or propositions. This point was anticipated (Gregory 1991) by the suggestion that the commands could be converted into parallel statements. Thus, "Discharge patient" could be converted into "The command Discharge the patient has been obeyed" or simply "The patient has been discharged". Similarly we can substitute "Treatment has been applied" for "Apply treatment", and "Treatment has been prescribed" for "Prescribe treatment". This gives Figure 2 which can be expressed in the propositional calculus as: $(p\to q)\And (q\to r)$.
But Probert still does not find this satisfactory. His argument (1991, p. 147) can be paraphrased as follows "the patient has been discharged does not logically entail treatment has been applied." His point depends on what we take $p\to q$ to mean. There is a certain ambiguity here that can only be resolved by using predicate logic.

#### The hidden premise

If we add a universal statement to the two statements given above, the problem is resolved: Major Premise: All cases where a patient has been discharged are cases where treatment has been applied. Minor Premise: A patient has been discharged Conclusion: Treatment has been applied (by Modus Ponens) Here we have the classic syllogism in which the major premise is a universal, the minor premise is a particular, and the particular conclusion follows by Modus Ponens. Probert's argument is that the conclusion here cannot logically follow from the minor premise without the major premise. This means that the model shown in figure 2 is a logically contingent argument. It is not, as it stands, a logically valid argument. The universal given above is a hidden premise in the argument that the figure represents. It can be noted that this will usually be the case with figures such as figure 2. The statements in these types of figure are always particulars. It it is unusual that a particular conclusion can be drawn from particular premises. Normally a particular will be deduced from a particular premise and a universal premise. An exception is simple conjunction, we can deduce "Socrates is a tall man" from the particular premises "Socrates is a man" and "Socrates is tall". Although figure 2 is not logically valid it is not false, and it can be made into a logically valid argument by adding universals. This can be done using the predicate calculus:
Domain: Hospital patients Fx: x has been discharged Gx: x has had treatment Hx: x has a treatment prescribed
1 Prem $(\forall x)(Fx\to Gx)$
2 Prem $(\exists x)(Fx)$
3 $(\exists x)(Gx)$ From 1 and 2 by Modus Ponens
4 Prem $(\forall x)(Gx\to Hx)$
5 $(\exists x)(Gx)$ From 3
6 $(\exists x)(Hx)$ From 4 and 5 by Modus Ponens
This can be rendered in English as follows: 1 For all patients, if a patient has been discharged then that patient has had treatment. 2 At least one patient has been discharged. 3 At least one patient has had treatment. 4 For all patients, if a patient has had treatment then that patient has had a treatment prescribed. 5 At least one patient has had treatment. 6 At least one patient has had treatment prescribed. The first three lines here repeat the syllogism given above. To this is added, at 4, another universal premise. Given this we can deduce 4. This is illustrated in figure 3 where the elements from figure 2 have been expressed in the predicate calculus and the two universals have been added; the arrows have been included only to show the general flow of the argument. The example given here is a simple one because the domain contains only one type of object and the predicates are all one placed predicates. However, this does not effect the argument as the numerous distinct objects and n-placed predicates can be dealt with in essentially the same way. It is significant that with the universals included in this way, the arrows from figure 2 are no longer necessary. The universals replace the arrows. It is no longer necessary to state $(p\to q)\And (q\to r)$ because this is contained in the two universals. The whole of figure 1, and any other conceptual model, can be expressed entirely in terms of universals.

#### SSM models as universals

An interesting fact about universals is that they do not, in themselves, commit us to the existence of anything. $(\forall x)(Fx\to Gx)$ does not imply that anything exists. It could just as easily represent "All unicorns eat ambrosia", which does not imply the existence of unicorns or ambrosia. It is not until we add a particular statement that there is any commitment to existence. That is why $(\exists x)$ is called the existential quantifier. In the argument above, existential commitment begins with $(\exists x)(Fx)$, the fact that there has been at least one patient who has been discharged. Once existence has been introduced existential consequences follow, such as $(\exists x)(Gx)$, the fact that at least one patient has had treatment. Expressing SSM Conceptual Models in universals ties in well with the idea discussed above: that the models are models of concepts not models of what exists, necessarily, in the real world. The predicate calculus highlights this distinction and shows that the model will only map on to the real world if a set of particular statements are true. This prompts epistemological questions that will be fully addressed in a later section.

#### Knowledge Based Systems

A direct information systems application is now apparent. The type of formula given above has an immediate counterpart in Prolog programming. The universals correspond directly to Prolog "rules". Lines 1 and 4, above, would be:
has_treatment (X) :- is_discharged (X).
has_treatment_prescribed (X) :- has_treatment (X).
the particulars would correspond to Prolog "facts". However, there could not be a direct counterpart to the existential quantifier. A Prolog program requires a value for the x in $(\exists x)$; to put it more precisely, there must be an instantiation instead of the object variable in a Prolog program.
In the example, this would be satisfied by naming a person, say Socrates, who is discharged:
is_discharged (socrates).
Given this Prolog "fact", the program will return the answer "socrates" when asked who has had treatment prescribed. This, therefore, is a rudimentary Knowledge Based System. Such systems would become much more elaborate, and useful, if based on larger models. For example, some of Wilson's models contain over a hundred elements. They would also be more useful if they embodied models that contained more complex logical relations such as the logico-linguistic conceptual models proposed in an earlier paper (Gregory 1992b).
It can also be noted that there are parallels between universals and field structure, and between particulars and records, in traditional data base design. There are, therefore, good indications that a relational data base design can be derived from these predicate calculus formulas or from the Prolog rules.

### Universals and the Status of SSM Models
#### Inductive hypotheses

Expressing SSM conceptual models in terms of universals escapes logical objections and thereby solves the immediate problem. Nevertheless, difficulties remain because the universals are, as they stand, contingent. All we have done is swap a contingent model in the propositional calculus for a collection of contingent universals. The status of the model will, therefore, depend upon where these universals come from. The most natural answer would be that they are "factual statements", that is, inductive hypotheses about the real world and based on real world experience. But in this case it would be the same as the Multiview model - a model that is conceptual rather than a model of a concept. However, this conclusion can be avoided because the universals in the model need not be inductive hypotheses. We can distinguish two other types of universal, these are value statements and definitions.

#### Value statements

Value statements include statements about personal tastes, such as "all of Shakespeare's plays are rubbish", and moral statements, such as "everyone ought to give to charity". Value statements can be distinguished from factual statements by a number of logical and epistemological properties. Evidence can be used to support or falsify factual statements but not value judgements. "All swans are white" is given supportive evidence by the observation of more and more white swans, and it falsified by the observation of one black swan. There is no evidence for "everyone ought to give to charity" nor can it be falsified empirically. Value statements connote a certain form of behavior. If Icabod believes that "everyone ought to give to charity" then Icabod will approve of charitable acts. Although they cannot be falsified empirically, two value statements can be shown to be incompatible with each other when they connote contradictory behavior. Factual statements do not connote any form of behavior.
From the logical point of view it is plausible to construct conceptual models entirely out of value statements. We can imagine what this would look like. With the universals "All people who drop litter are bad" and "All bad people should be punished", and an instantiation, "Icabod drops litter", we can draw the conclusion: "Icabod should be punished". Value statements alone, will not, of course, account for the models that are, in fact, produced in SSM. There is no way that "All cases where a patient has been discharged are cases where treatment has been " could be construed as a value statement.
SSM prides itself on being able to deal with the human aspect of a problem situation. It is, therefore, surprising to find that value statements have a very small role in the building of conceptual models. Value statements are usually implicit in the criterion for effectiveness and they can sometimes, but not always, be found in the Weltanschauung part of CATWOE. Apart from this they rarely appear. Despite the fact that the models are constructed in the language of imperatives these almost always turn out to be practical rather that value ridden imperatives. They are of the form "You should turn left if you want to get to the station" rather than "You should give to charity if you want to be good".
Another crucial difference between value and factual statements is that value statements are not reducible to factual statements and factual statements are not reducible to value statements. What this means is that we cannot derive factual statements from value statements. If we are to draw a factual conclusion we must have at least one factual premise, factual conclusions cannot be drawn from value statements alone. The same is true of value statements, a conclusion that expresses a value cannot be derived from purely factual premises. This point is summed up in the dictum "you cannot derive ought from is". Given this and SSM's anti-reductionist stance, it is even more surprising that value statement have such a small role to play in the models.

#### Definitions

If we accept that SSM conceptual models are not intended, in any straight forward way, to be models of things that are in the real world, then we are forced to the conclusion that the universals must be definitions. A distinction is made between definitions intended to establish an existing meaning, descriptive definitions, and definitions giving a proposed meaning for the future, stipulative or prescriptive definitions.
Taking the SSM universals to be descriptive definitions has an initial plausibility. In this case the conceptual models would not be models of the real world but models of a language used to describe the real world. This could account for a lot of what happens in practice. Organizations tend to develop their own languages. The process of SSM conceptual model building could be taken to be a process whereby the stake-holders describe how this language is used. But if this were all that was going on the process would be quite simple and there would be no need for a lengthy iterative debate about the model.
Taking the SSM universals to be stipulative definitions is much more plausible. In this case the building of conceptual model is a process whereby the stake-holders come to agreement about how to use words to describe the problem situation. The model building would, therefore, not consist just of describing an existing language, but of making one up. This would not, of course, entail that the language would be significantly different from the one already in use. It would entail that ambiguities were removed and different usages on the part of different stake-holders would be brought out and resolved.
In this way the model building process can be seen as a type of Wittgensteinian language game. Wittgenstein's later account of language draws heavily on an analogy with games such as chess. Such games get their meaning from a set of agreed rules. This principle could apply to conceptual models. Figure 1 can be interpreted as a set of rules for the use of a language within a particular organization. The universals given in section 4 could be expressed as rules:
Rule 1: Nothing is to be described as "a discharged patient" unless it is preceded by something that can be described as "an application of treatment".
Rule 2: Nothing is to be described as "an application of treatment" unless it is preceded by something that can be described as "a prescription of treatment".
This account of conceptual models in terms of stipulative definitions fits well with the main thrust of SSM which is to address unstructured problems. Unstructured problems come about not because of a lack of structure in the real world but because of a lack of structure in descriptions of the real world. The creation of a cohesive set of definitions can provide the structure. For example, if we want to find out if all Christians know the Bible, then the main methodological problem is going to be deciding what Christians are (People who say they are? People who go to church regularly?) and what is meant by "knows the Bible" (All of it? Most of it? Some of it?). Once these things have been decided, collecting the real world data will be, methodologically, fairly simple.

#### SSM models and the real world

If the universals that constitute the SSM models are definitions, then it follows that the models will be analytic rather than synthetic. That is, if they are true they are true by the meaning of the words alone. If this is the case, there is nothing in the conceptual model building process that guarantees that the models can refer anything that exist or could exist. There is nothing that prevents them from including references to unicorns, Greek gods and flying pigs. Obviously, models that contain these types of reference cannot be used as a basis for information system design or for organizational restructuring.
Similar problems will arise for those people who consider that the only point in building a conceptual model is to change peoples' thinking. This is because a change in thinking can only be useful if it contains a reference, directly or indirectly, to an actual or potential real world state of affairs. Pragmatic and verificationist theories of meaning hold that without such a reference a change in thinking is not just useless but is, literally, a meaningless notion (see for example Ayer 1946). The same can be said about values; if a change in values does not indicate a change in behavior in response to some actual or potential event in the real world, then it is pointless to say that there has been any change in values.
Establishing how an analytic system, such as arithmetic, maps on to the real world is the subject of complex and contentious theory. In the case of a conceptual model, such as that represented in figure 3, we would need to establish a an instantiation for the object variable $(\exists x)(Fx)$ , i.e. that Socrates, or some other person, is discharged. Having established that Socrates is discharged, we can establish deductively that Socrates has had a treatment prescribed; this is true by definition. But if it is true by definition it cannot be true that Socrates is discharged and false that Socrates has had treatment prescribed. Therefore, in order to be sure that Socrates is, in fact, discharged we must be sure that he has had a treatment prescribed. But if we must be sure that Socrates has had a treatment prescribed before we can be sure that Socrates is discharged, then the deduction that Socrates has had a treatment prescribed tells us nothing new.
Problems of this order are the basis of the claim by some empiricists that tautologies tell us nothing about the real world. However, this would appear to be false because arithmetic is an analytic system, true by definition and a tautology, but arithmetic appears to tell us a lot about the real world. This vicious circle can be avoided if there is an independent criterion for a patient being discharged, that is, a criterion that is not a definition. Suppose the completion of Form PQ7 is such a criterion. The relation between Socrates is discharged and Form PQ7 has been completed for Socrates will be a contingent relation. Let us further suppose that there is a similar criterion for a patient having a treatment prescribed, say, the completion of Form RX5. Now, we find that Form PQ7 has been completed for Socrates from this we infer, contingently, that Socrates is discharged; from this we deduce that Socrates has had a treatment prescribed; and from this we infer, contingently, that Form RX5 has been completed for Socrates.
From this we can see how an analytic system has proven useful. It has allowed us to infer one contingent event from another, events that might otherwise not have been connected. But a stronger case than this can be made. It can be argued that definitions are not only useful for contingent inferences, they are logically necessary (see Definitions & inductive hypotheses below).

#### The limitations of SSM

The essential problem for SSM is that there is no logical reason why the stake-holders should come up with Conceptual Models (a set of definitions) that map on to the real world. Connected to this is the fact that SSM has no why to determine whether or not these do or do not map on. It could be argued that the real world contingency is introduced at a later stage. In Wilson's method the real world seems to begin to enter when information inputs and output between activities are identified. However, it is not altogether clear whether these are meant to be notional information input/outputs between notional activities, or real world information input/outputs between real world activities. In either case there is still a problem. If the information input/outputs are notional we still have to establish that they can map on to the real world. If they are real world information input/outputs between real world activities, where did the real world activities come from? How was it established that the notional activities from the Conceptual Model map on to real world activities?

### Universals and the Status of Multiview Models
#### Definitions & inductive hypotheses

The importance of establishing definitions for universals will be readily apparent when it is realized that there is no intrinsic way of distinguishing between definitions and inductive hypotheses or a fool-proof intrinsic way of distinguishing between definitions and value statements. Given that a certain universal is not a definition we can tell whether it is a value statement or an inductive hypotheses by certain key words that indicate values rather than objective facts about the real world. These include "should", "ought", "good", "bad", "nice", "nasty", etc. There is no set of words that can identify a definition.
Today "all men are mortal" would be considered an inductive hypothesis by most people. Most people would be likely to say that men are mortal because it has been observed that every man has died before, say, his 200th birthday. But for the Greeks "all men are mortal" was part of the definition of a man. The Greeks thought that some men-like beings lived for ever, but these were not "men" they were Gods. For us, "immortal men" is meaningful, it stands for a class that happens to be empty; but for the Greeks "immortal men" was a contradiction in terms.
Value statements entail certain forms of behavior. From the use of the key value words in a given utterance a certain form of behavior will normally, but not always, follow. If Icabod says "all Christian are good people" then, if his utterance was sincere, we would expect Icabod to approve of Christians and act appropriately; if this is the case then Icabod's utterance was a value statement. However, Icabod might have made the utterance sincerely yet disapprove of Christians, we can imagine that Icabod prides himself on being a bad person; in this case the utterance was not a statement of Icabod's values but part of Icabod's definition of the words "Christian" and "good".
A distinction can be made between intensive and extensive definition. An intensive definition gives the sense (connotation) of the definiendum. An extensive definition gives the reference (denotation) of the definiendum. In terms of classes an intensive definition will provide a criterion of class inclusion whereas an extensive definition will list all the members of the class. Thus, an intensive definition of "a human limb" would be any jointed appendage on the human body, an extensive definition would be an arm or a leg.
An argument that definition is logically prior to inductive hypotheses can now be put forward. Empirical evidence of class inclusion require that the class is defined independently of that evidence. For example, if we say that all panthers are black then, if this is to be an empirical statement, there must be defining criteria for panthers that are independent of their colour. If being black is one of the defining criteria for panthers then "all panthers are black" must be analytic and cannot, therefore, be empirical.
As a matter of fact, being black is a defining criterion for panthers. "Panther" is just the word for a black leopard. So, to say that "panthers are black" is just to say that "black leopards are black" and this cannot be established empirically. As it is logically impossible to observe a black leopard that is not black, observation could never falsify the statement "black leopards are black"; as observation can never falsify the statement, observation cannot provide inductive evidence for the statement either.
If a term has been given an intensive definition we can establish the extension of the term empirically. Thus, if we intensively define "human limb" as any jointed appendage on the human body, then it can be established empirically that all human limbs are arms or legs. Likewise, if a term has been given an extensive definition we can establish the intention of the term empirically. If we extensively define "human limb" as an arm or a leg then it can be established empirically that all human limbs are jointed appendages on the human body.

#### Constraints on the Multiview model

Having answered the immediate logical problems facing the SSM model by a somewhat tortuous route, it is appropriate to point out that the Multiview model is not as simple as it might seem. At first glance the Multiview model seems to be a generalized model based on observation and as such theoretically unproblematic. On closer examination the model involves considerable logico-linguistic difficulties.
Figure 4 is a Multiview conceptual model taken from a case study for a Distance Learning Unit. The large arrows represent flows of physical things, the small arrows represent information flows between the subsystems. If this was a model of an existing Distance Learning Unit it would not be problematic, nor would it be interesting. It would just be a generalized version of a materials flow diagram and a conventional data flow diagram. However, in this particular case the Distance Learning Unit did not yet exist. The Conceptual Model was, according to Avison & Wood-Harper, derived from a root definition. This root definition was:
"A system owned by the Manpower Services Commission and operated by the Paintmakers Association in collaboration with the Polytechnic of the South Bank's Distance Learning Unit, to provide courses to increase technical skills and knowledge for suitably qualified and interested parties, that will be of value to the industry, whilst meeting the approval of the Business and Technical Education Council, and in a manner that both efficient and financially viable." (Avison & Wood-Harper, 1990)
We can express the double headed arrow between Administration System and Course Exposition System in figure 4 as "there must be a mutual flow of information between an Administration System and a Course Exposition System". How could this be derived from the root definition?
As with the SSM model there must be a hidden premise. This would be "Whenever there are courses to increase technical skills etc. there will be an Administration System and a Course Exposition System and a mutual flow of information between them". This is, of course, a universal. We can now ask: where does it come from? As Multiview statements are at the second level, referred to in section 3, it must be an inductive hypothesis based on the observation of other courses.
As we saw above, inductive hypotheses cannot be separated from definitions. The universal here would seem to specifying part of the extension of the term "courses to increase technical skills etc." this assumes that there is an intensive definition of the term. "Technical skill" needs to be defined outside of the full extension of the term "courses to provide technical skills etc.". "Technical skill" could not be defined in terms of passing the exam, for example; because, in this case, the only thing that "technical skill" would mean would be that the exam was passed. "Technical skill" needs to be defined in terms of some external factor such as the ability to paint a fence (presuming that painting a fence is not part of the extension of the word "course").

#### The limitations of Multiview

There are two possible ways in which Multiview can work. One is where the stake-holders already have a well defined common language. The other is where the definition that an information system requires develop informally during Multiview systems analysis. The danger with Multiview is that in any given application the common language may fail to exist and may fail to develop. This danger is compounded by the fact that Multiview does not have the means to determine whether the common language is there or not. The Danger can be avoided if definitions were included into the Multiview model building process.

### Conclusions
#### Solutions to the SSM Problem

One solution to the SSM dilemma is to take the model as consisting of a set of definitional universals which will map onto the real world if there are instantiations of certain particulars. This is the position advocated, though not in exactly the same terms, in two previous papers (Gregory 1992a, 1992b). Ideas can be put forward to indicate that this is theoretically tenable. One is that it would mean that the SSM models had the same status as other analytic or axiomatic systems and many of these, such as arithmetic, have proven very useful. The problem here is that not all axiomatic systems do map on to the real world (see Hofstadter 1979). However, by using independent criteria for the particulars we can establish whether or not the model does or does not map on to the real world. In effect this make the model one large inductive hypothesis (the question of whether arithmetic is also a large inductive hypothesis will not be addressed here!). The problem here is not theoretical but practical. The idea of an analytic model is difficult explain to many people. For example, the development of the models often requires the use of a number of extensive definitions (see Gregory 1992b). Extensive definition is quite respectable (see Copi 1971), but some people find it difficult to accept that an extension could be anything other than empirical. Another problem is a lack of flexibility. The model building process is unable to draw upon a large body of generally accepted facts. There is, however, another theoretical possibility and that is to integrate the definitions and inductive hypotheses to form a mixed model.

#### Possibility of a mixed model

A mixed model could expressed entirely in universals and combine the linguistic capabilities of SSM with the empirical grounding of Multiview. Care would need to be taken to distinguish between definitions and inductive hypotheses. This could be accomplished using model logic. The definitions would be flagged as necessarily true while the inductive hypotheses would be flagged as probably true. A new dimension could be added by including numerous value statements determined by a consensus of the stakeholders. These could also be flagged as necessarily true as the determination of values is not part of the role of a computerized information system. Such a model need not be limited to the passive representational form of conventional conceptual models. It could be a dynamic model - a calculus of particular statements.

#### Acknowledgments

The findings in this paper were the result of research funded by the Science and Engineering Research Council (SERC).

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