by

Warwick Business School,

University of Warwick

Coventry CV4 7AL

TEL: 0203 523523 Ext. 2393

FAX: 0203 523719

May 31, 1992

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.

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 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 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 --> q) & (q --> 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 --> q to mean.

There is a certain ambiguity here that can only be resolved by

using predicate logic.

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 ( x) (Fx --> Gx)

2 Prem ( x) (Fx)

3 ( x) (Gx) From 1 and 2 by Modus Ponens

4 Prem ( x) (Gx --> Hx)

5 ( x) (Gx) From 3

6 ( 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 --> q) & (q --> 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.

An interesting fact about universals is that they do not, in

themselves, commit us to the existence of anything. ( x) (Fx

--> 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 ( x) is called the existential quantifier.

In the argument above, existential commitment begins with ( 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 ( 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.

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 ( 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.

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 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.

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

goes 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.

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 ( 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 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?

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.

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").

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.

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.

6.2 Potential for 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.

7 Acknowledgments

Acknowledgments

The findings in this paper were the result of research funded by

the Science and Engineering Research Council (SERC).

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