How Formal Logic Can Fail
to be Useful

for Modelling or Designing MAS

Centre for Policy
Modelling

Manchester Metropolitan University

http://cfpm.org/~bruce

*“To a person with a hammer, every screw looks
like a nail” *(trad.)

**Abstract.** There is a certain style of
paper which has become traditional in MAS – one where a formal logic is
introduced to express some ideas, or where a logic is extended on the basis
that it then covers certain particular cases, but where the logic is not
actually *used *to make any substantial inferences and no application of
the logic demonstrated. I argue that
although these papers do follow a certain tradition, that they are not useful
given the state of MAS and should, in future, be rejected as premature (just as
if one had simulation but never run it).
I counter the argument that theory is necessary by denying that the
theory has to be so abstract. I counter
the argument that logic helps communication on the simple grounds that for most
people it doesn’t. I argue that the
type of logic that tends to be used in these papers is inappropriate. I finish with some suggestions as to useful
ways forward.

Introduction

During RASTA 2002 there was some discussion about the utility of formal systems for building or understanding multi-agent systems (MAS). This paper is an attempt to put my arguments. I argue that (as with any tool) one has to use formal systems appropriately. Merely following a tradition of how to use and develop a particular kind of formal system is not sufficient to ensure one is doing something useful.

In this context I wish
to make it clear that I have nothing against logic. I like formal logics because they can deal with qualitative
information and they can be quite expressive. However, at the end of the day^{[1]}, they are just one of a range of types formal
systems that could be used – the kind of the system that is chosen is
important. The point is to distinguish
when and how a particular formal system is useful – this applies to formal
logics as a particular case.

In short, the question
is not whether to abstract from our field of study using formal systems but
how. In the past, premature ‘armchair
theorising’ has not helped the eventual emergence of useful theory, but rather
impeded it. Formal systems (such as
logics) are not the *content *of theory but merely a *tool *for
expressing and applying theory in a symbolic way – choosing the wrong kind of
formal system will bias our attempts and make our task more difficult.

Two 20^{th}
Century Trends in Logic

Whitehead and Russell (1962)
showed that set theory, arithmetic and a good chunk of other mathematics could
be formalised using first-order classical predicate logic. This dramatically demonstrated the
expressive power of logic. Once set
theory was properly logically formalised and the expressive power of set theory
revealed it became clear that all mathematics could be embedded in set theory
and hence be logically formalised. If
any system could be shown to have an embedding in set theory, then it counted
as mathematics. Thus set theory and
classical first order predicate calculus was shown to *general systems*,
in the sense that all known formal systems could be expressed in them (albeit
with different degrees of difficulty).

In the second half of
the 20^{th} Century there was an explosion of different kinds of
logic. This can be divided up into two
approaches: those who were searching for the ‘one true logic’ (what I call the
‘philosophical approach’); and those who saw logic as merely a useful tool for
doing complex inference (what I call the ‘pragmatic approach’). The former of these tinkered with the very
structure of logic, restructuring the nature of deduction in the logic so as to
match correct inference in natural language and by inventing new objects into
the logic such as indices, operators, names etc. The nature of their discussions went very much by example – since
they felt it was worth trying to construct the ‘one true logic’ it necessarily
had to include all such cases. Logics
in this vein included intuitionistic logic, free logic, relevance logic and
modal logic. Due to the nature of their
discussions their work tended to concentrate upon the axioms of the logic in
relation to particular cases and treat the proof theory and formal semantics
more as an after thought.

The pragmatic approach
does not care so much about the philosophical interpretation as to what could
be done with the logic. Thus, since
classical first order predicate logic was generally expressive (Gabbay 1993),
they tended to work within this framework or construct simple extensions of
it. For these people it was the
pragmatic virtues that mattered: was it good for doing inference in; were its
formal semantics checkable; was it easy to model with; and could it be used for
computation (ala Prolog and its successors)?
The particular logic chosen for the MAS modelling language, SDML^{[2]} is a case in point – its purpose is not to
capture any general theory of cognition but to provide a sound and efficient
basic for the consistent firing of complex sets of interdependent rules (Moss
et al. 1998).

Unfortunately the philosophical approach has tended to attract the more attention in AI. There may be many reasons for this: it may be that the association with philosophy gives it academic status; it may be that the participants truly believe that there will be general logical systems that encode cognitive relations in ultimately simple ways; and it may be that it is relatively easy to do but difficult to criticise. Whatever the reason there has grown up a tradition in AI (and now MAS) which discusses and compares different axiomatisations of logic and logical systems based purely on plausibility and the ability to encode particular examples (i.e. its expressive power). It is this approach that I am arguing against on the grounds that it will not be useful in either understanding or building MAS.

Generality and Abstraction

One of the principle ways of
achieving generality is to abstract away from the detail of particular cases
leaving only what happens to be true of the wider domain one is considering
(post hoc abstraction). Another way is
to decide the structure before hand and to *choose *one’s domain
accordingly or else to simply ignore those aspects of those cases that seem to
contradict that structure (a priori abstraction). A third way is to include a method for adapting to the
particularities of each case so that the detail is preserved (adaptive
generality). However it is achieved,
the increased generality is obtained at a cost, a cost of lost information,
relevance or computation respectively.
The cost of losing information as a result of post hoc abstraction may
be critical if it is the important details (w.r.t. one’s goal) that are lost. The cost of restricted relevance as a result
of a priori abstraction may be critical if this means that it excludes your
intended object of study. The cost of
increased computation may be critical if the computation is too onerous to be
practical.

One well-known dynamic
of philosophical discourse is that of the counter-example followed by an
increase in generality: a thesis is proposed; then a case exhibited where the
thesis fails; and, in response, the thesis is generalised (e.g. by adding
caveats, or by being suitably elaborated).
The repeated application of this process of a priori abstraction is a
set of very general, but irrelevant principles. These principles may give one the illusion of relevance because
the ‘ghosts’ of the original concepts are left as labels and symbols in the
general principles and one has the impression that the relevance can be
restored by the simple adding of particulars.
However, if this attempted this is found to be unworkable in
practice. Be clear – it is not
generality or abstraction by themselves that causes this lack of relevance but
the *way *the generality is achieved (i.e. a priori abstraction). Similarly – I am not arguing against
generality or abstraction but that it should be done in a way that results in
useful theory. Work which attempts to
mimic the counter-example-generalisation process in formal logic will not
result in relevant theory about MAS.

One way of clearly
demonstrating that increased generality is not a sufficient reason for
exhibiting a logic is that there are already many logics (and other formal
systems) that are as general as possible.
If a particular logic has the ability to capture a particular concept
then the general one will also be able to do this. The point of inventing new formal systems is thus *entirely*
pragmatic, for each system (even the general ones) will inevitably facilitate
the construction of certain systems and frustrate others, just as different
programming languages are good at certain tasks and bad at others. This presence of implicit bias is not a
question of the theoretical ability of the system but practical ease for us
humans. This is why we neither
formalise everything in set theory nor program using Turing Machines. Choosing an inappropriate formal system will
bias the development of a theory in unhelpful ways, choosing an appropriate
system will facilitate it (Edmonds 2000).
Merely establishing that a particular system can express certain
properties does not demonstrate that the system will facilitate a good theory,
for the general systems also do this and they would (almost certainly) make
formal modelling impossibly cumbersome and inference infeasible.

Thus arguing for a
particular kind of formal logic on the grounds that it is able to express
certain ideas, concepts or cases is very weak, for there are already formal
logics that do the same (if any can).
Thus, although the development of formal logics is often driven by a
wish to express certain ideas, they need to be *justified *on other,
stronger grounds.

The Need for Theory

Clearly if we are to escape
simply considering individual cases and if our understanding of MAS is to
inform our construction of MAS (and *vice versa*) then we will need to
generalise and abstract our knowledge, i.e. use ‘theory’. The trouble is that ‘theory’ can come in a
variety of levels of abstraction and a variety of forms. A natural language description is already a
sort of theory because it is the result of many relevance and representational
decisions – it provides a level of generalisation by facilitating the
comparison of phenomena by substituting the comparison of descriptions. An MAS may be also be used as a method of
producing a sort of dynamic description of a social system – this is when one
attempts to program the individual agents as closely to actual accounts as
possible and then check that all stages also correspond to those in the social
systems at all levels of aggregation.
Another MAS may be intended to represent a set of phenomena that occurs
in a small set of individual cases – here the generality is restricted to a
particular domain. At the other end of
the scale are the ‘high theories’ of philosophy or sociology – these are ideas
that are supposed to have a very great level of generality. In philosophy the theories tend to be
precise but irrelevant. In contrast, in
sociology the theories are relevant but often extremely difficult to pin down –
they are more akin to a richly expressive language for talking and thinking
about social phenomena.

I am unsure of exactly
what Rosaria Conte means by ‘theory’ during her remarks during the closing
panel of AAMAS 2002 (and elsewhere). If
she meant that *some* level of abstraction will be necessary for escaping
from individual cases, then I agree with her – simply constructing particular
MAS is not enough. However, if she is
arguing that ‘high theory’ is necessary, then I disagree, for intermediate
levels of abstraction also allows us to escape from single cases. For example physicists managed perfectly
well to develop useful theories before the advent of their high theories,
indeed they are still looking for a ‘Theory of Everything’ (TOE), even though
it is clear that the situations in which such a TOE would diverge from the more
mundane theories we already have will be extreme and unusual (from our point of
view).

In the past theory that is mainly based on intuition which overtakes its evidential warrant has not had a good track record in resulting in useful theory. In fact, there is evidence that it has actively hindered the development of useful theory. A classic example of this is the thought of Aristotle on anatomy, which was wrong but played a part in delaying the spread of accurate information derived from dissection. Part of the reason for this is that theories play an important role in providing a language for thought, which (amongst other things) effects what evidence we look for (Kuhn 1962) and biases further modelling effects (since other kinds of models will probably not fit well in that framework).

Thus papers proposing ‘high theories’ of MAS need substantial justification before being trusted and certainly more than a few cases and vague intuitions. Further, such high theory is unnecessary in order to escape particular cases and experiences – models that are specific to particular kinds of MAS and only somewhat abstract may be at a more appropriate level of abstraction and hence more reliable.

Different Stages of Science

If a particular language of thought is correct in the sense that its structure is itself well validated, then it might be well be profitable to explore. This is the situation that prevails in what Kuhn (1962) called ‘normal science’ – a theory has been discovered and validated and then there is a stage of exploring the ramifications of this theory, applying the theory and using the theory as a means of guiding the search for new theories. This stage of science can be characterised as relatively cooperative and inward looking time – the participants tend to specialise into complementary skills and tasks and put these together within the established framework. There is a lot of ‘building’ on each other’s work and the field establishes norms so that new entrants to the field are required to strongly situate their contribution within the established framework, for example by citing those considered authorities. This can have the effect of excluding outside ideas so that the field becomes inward looking. In extreme cases this results in the ‘degenerate programmes’ described in (Lakatos 1983).

During a period of normal science it may be sensible to simply accept the established principles, methods and assumptions and to concentrate on specialising and then developing complementary areas of knowledge using them. During such a time when those in the field are all using the same framework and outsiders are rare, one can take the common language of the participants for granted and simply use it as a vehicle for discussion.

Occasionally normal science is punctuated by periods of ‘revolutionary science’. This is when the established framework (if any) has become (or is revealed as) unsatisfactory and if a new and better framework is introduces it may become accepted. During such a period very little can be taken for granted, especially the assumptions and methodology of the old framework. Instead of cooperation and complementarily, sharp competition between different ideas and methods dominates. Contributions are judged less by adherence to a particular framework and more by results. Typically in such periods one gets many contributions and academics from other fields being both offered and accepted.

During periods of revolutionary science one can not merely carry on with ‘business as usual’. Contributions to knowledge need to be more thoroughly justified in terms of results and (since there is likely to be a diverse audience) explained without assuming that all will understand the same language of expression. Since even the framework is in flux, what the relevant authorities for citing are unclear and it is not necessarily helpful to use established methods.

Neither the simulation
of MAS nor their design has an established and well validated framework. There is no ‘high theory’ of MAS, and no
proven methods. Whilst it is true that
some people have *claimed *the status of authorities, whether posterity
will agree will depend upon how useful their contributions turn out to be. A paper that might well be acceptable by
those inside a field during a period of normal science can be found wanting in
periods of revolutionary science, especially in the extent to which it
justifies its method and proves its usefulness through its results. (Edmonds 2000) discusses the relationship
between formal systems and the dynamics of science in more detail.

A confusion about the
stage that MAS is at may explain why some authors present their papers as they
do – borrowing the style rather than the substantiality of papers in more
successful sciences. If MAS did have a
well validated general theoretical framework, then it might be more acceptable
to present a exploration of part of that framework in a theoretical way,
copying the methodology of accepted authorities in the field. Indeed, some of these papers *do* seem
to imply that the use of simplistic deontic and epistemic logics *have*
been established and proven, so what is left is to argue the details and make
small extensions of these.
Unfortunately this is far from the case – this style of formalism still
has everything to prove.

What Sort of Logic is Suited for Modelling MAS?

Since, in common with many
other styles of formal system, logic has the possibility of modelling any
system (via the truths concerning that system), it not so much a question of
whether logic per se is or is not the correct kind of system, but more the
particular type of logic that is used^{[3]}. In particular
it has tended to be the axiomatics of non-temporal, context-independent and
propositional logics which are commonly discussed in this domain. This is in keeping with the philosophical
logic tradition briefly discussed above.
However, it seems patently clear that, if one is going to use formal
logics in this domain, that it is the formal semantics of temporal, and
contextual predicate logics that are far more appropriate. I consider these aspects in the following
subsections.

Time

There are many ways of
interpreting what logic *is* – as many ways as there are of interpreting
the syntactic systems that constitute formal logic. Some see it as a way of defining a set of truths using inference
or formal semantics, others see the inference as the most important which can
be used for inference of conclusions (including the set of truths). Different people put the emphasis on
different parts (which they may see as primary) and see the other parts as
coming from these. However you see it
logic relates a class of *truths* with a system of *inference*^{[4]} (embodied either in the proof theory as
allowable steps or as the formal semantic validity of expressions expressing an
implication).

As such it is hard to
see how a logic can usefully model the connection between goals and actions
without including an explicit representation of time. For example, the relation between the goal indicated by the
utterance “I want to go for a walk tomorrow” and the present action of “cancelling
a meeting scheduled for tomorrow” has an important temporal element to it. Yet almost all of the logics that have to do
with goals and actions (including the deontic and BDI logics) do not have any *explicit
*temporal element, instead they attempt to capture either the instantaneous
or unchanging aspects in the relationship between such as: beliefs, desires,
norms, goals, actions. In the first case they must miss the dynamic nature of
the relationships, for example that one might change one’s intentions as the
result of weighing the effect of violating a social norm – indeed such an
approach rules out any *interaction* between these entities at all. In the later (unchanging) case, one is
limited to modelling only those aspects of the relationship that are always the
case – thus if sometimes (but not always) a belief changes a desire and
sometimes (but not always) a desire changes a belief then these relationships
will not be universal over time. In
this case it is an implicit assumption that the important relationships *are*
abstractable without reference to temporal contingencies, which is extremely
unlikely and without justification^{[5]}.

The other approach is
to use implication as an implicit model of causation and thus encode the
relevant sequencing in the axioms. The
result of trying to fudge the issue in this manner is that the essential
elements of the situation are represented by ludicrous propositions such as *A*
= *the assertion that state of the world is such that I will be walking
tomorrow* and *B *= *the assertion that I will take an action which I
believe will prevent a future event which would imply **Ø**A* . This sort of move does
nothing to convince me that this method of formalisation is capturing the
essence of the case. Yet this is the
case with many attempts which attempt to concertina concepts which are
temporality situated into a non-temporal framework – representing *processes*
as *single states* is bound to lead to huge practical difficulties if the
framework was ever used for real problems.

Lack of Formal Semantics

Another strange fact
about the style of formal logic that have been discussed in RASTA and more
generally in MAS is the lack of formal semantics. If one is primarily concerned with the *meaning *of modal
operators and determining which ones are *valid *then the formal semantics
are much more relevant than the axioms and proof theory. A logic that had as its universe of models
(models in the logical sense) a set of MAS outcomes (i.e. the set of possible
MAS states over time) and showed that certain expressions were logically
validated w.r.t. these semantics, would be a useful development. On the other hand if one is more interested
in inference (being able to infer conclusions from premises) then the proof
theory is more important (in this latter case, one would expect minimal discussion
of the meaning of operators and a focussing on the useful and interesting
inferences that can be obtained using the proof theory).

Context Dependency

The typical presentation of logic in MAS assumes and depends upon the fact that all the reasoning is done within a single context. Sometimes this is explicit, but more often it is left implicit and only indicated by the test problems (if any). This is very strange because reasoning about norms, goals, intentions, learning is only feasible if one can relate these to the contexts, for example intentions may involve action in several different contexts or involve explicitly effecting what the context is.

Numbers

A final area I will deal with is the ability of logic for understanding or designing MAS that does not allow for an adequate arithmetic. MAS in which numbers play no significant part are hard to find, but despite this most of the logics proposed rule out any sort of predicate logic in which such numbers could be defined. The reason for this is, presumably, because the introduction of arithmetic means that there can be no complete formalisation of truth, that is to say that there will be no method of proof that will be able to prove all the truths. This is due to Gödel’s incompleteness theorem. However, the goal of completeness is simply inappropriate for almost all MAS – we are never going to be able to prove all an MAS’s properties. Thus eliminating numbers to retain completeness is not sensible – it is a case of changing the problem to suit the tool.

Of course, a temporal contextual predicate logic with semantics that can capture multi-agent belief will not be such a clean simple system as those frequently discussed, but that is appropriate because most MAS are not clean simple systems! In this case simplicity is certainly not indicative of usefulness, let alone truth (Edmonds 2002). Some will argue is that they are deliberately abstracting away from the detail of time, context, and numbers in order to obtain a general theory, but the burden of proof is then surely upon them to show that they have done this successfully. Justifying such extreme abstraction on the basis of a few intuitions does not wash – the wish for the ‘magic’ shortcut is strong but can not be relied upon.

On the other hand, if proponents of such formalisms tried to use their constructions on real problems or to model real systems, the inadequacies and over-simplicity would be quickly revealed. If (as I suspect) there were no adequate work around that preserved the logic then this would be revealed and if there were it would be demonstrated how and in what way this formalism would work,

The Audience’s Viewpoint

When presenting results
there is an understandable wish on the part of the authors to concentrate on
what they have *done*. However,
for the audience it is more important to first of all judge whether the work is
worth learning about or even applying.
This is because they are bombarded with ideas people have had and
systems they have designed – they are not short of ideas, but they do need help
in deciding which ideas or systems to invest their time and effort in. Everybody feels convinced that their ideas
or systems will work, otherwise they would not be presenting them. Similarly,
everybody has some sort of thought train that lead them along the path they
took, so everybody has *some *good reasons for doing what they did. Thus the presence of good reasons for doing
something does not help an audience distinguish between different ideas or
systems, more is needed.

One claim for formal logic made during the discussion at RASTA 2002 was that it aids communication because it allows one to be precise about ideas. That they allow one to be precise is true, formal systems (even if totally misguided) at least make for an unambiguous common referent. This is particularly attractive for disciplines which are bedevilled by different approaches, vagueness and misunderstandings with respect to their key terms. Precision is definitely a virtue, but it is not sufficient to ensure good communication. Whether formal logic does or does not aid communication is an empirical matter. Frankly, I doubt whether this was true for the audience we had at RASTA, for these logic papers are only accessible to the small minority who had sufficient familiarity with formal logic to be able to fluently ‘read’ it.

Even if there we
assume that formal logic *did* aid communication between those who had
suitable training, this still is insufficient to justify such a
presentation. Being crystal clear in
one’s communication is no good if what is being communicated is not worth the
effort. What was being communicated in
some of these papers was simply unproved ideas and intuitions – directly
comparable to specifications for systems that have not been implemented or
otherwise tested.

Further the fact that the ideas and intuitions were expressed using formal logical expressions served to prevent the majority of the audience from evaluating them, leaving this evaluation to an ‘in crowd’ who are, on the whole, already sympathetic to the approach. It is almost certain that if I had not been there (being a person who is both critical and sufficiently knowledgeable of formal logic) there would have been no discussion about the worth of the formal logical approaches presented. Now I am sure that it was not the intention of the formalists to use their formalisms as a way of preventing criticism or ensuring acceptance, but this would have been the effect.

Thus a paper which
does not provide any evidence for the usefulness of a formalism (apart from the
reasons that lead the authors to invent or extend it) simply fails to satisfy
the justified norms of scientific communication because it ignores the needs of
the audience to evaluate the suggestions.
Further, a formal system that has been used for solving a real problem
or modelling a realistically scaled MAS will be greatly improved and be more
likely to introduce genuinely new ideas.
Intuitions are highly biased by the current *Zeitgeist* which is
why rubbing them against a real problem is more likely to provide new input
than simply more discussion between other academics immersed in the same *Zeitgeist*.

A Common Argument for Formalism

However, a logician (or mathematician or whatever) may object in the following manner: “the history of the development of formal systems has included many systems that would have failed on your criteria and yet turned out to be immensely useful later - are you not in danger of arguing against similar advances with such warnings?” My answer is fourfold.

· Earlier, we did not have the huge number of formal systems we have today, and in particular we did not have the general systems mentioned above. Today we are overwhelmed by choice in respect to formal systems – unless substantial advances are made in their organization all new systems will need to be substantially justified if their clutter is not to overwhelm us.

· There are proper domains for formal systems that are purely conceptual: philosophy or pure mathematics. Presenting a formal system elsewhere implies that it is relevant to the people in the domain in which it is being presented. If it really is relevant to them this needs to be demonstrated.

· Even in pure mathematics presentations or publications are required to justify themselves appropriate criteria - novelty, expressiveness and soundness are not enough (although the other criteria perform a weaker role than when they are applied elsewhere). For example, in the examination of a doctoral thesis in pure mathematics once the soundness of the work is deemed acceptable it is the importance, generality and relevance of the results that are discussed.

· The cost structure of the modelling enterprise has changed with the advent of cheap computational power. It used to be the case that it was expensive in both time and other resources to use and apply a formal theory, so that it was important to restrict which formalisms were available. Given that the extensive validation of the success of formal systems was impossible they had to be selected almost entirely on a priori grounds. Only in the fullness of time was it possible to judge their more general ease of use or utility of their conclusions. Now this situation has changed, so that the direct validational assessment of a formal system can be achieved with relative ease for relevant cases.

One can choose to judge a formal system by the criteria of pure
mathematics (or logic) that is show the system has generality and inferential
power by exhibiting theorems and proofs.
One can choose to judge it as applied mathematics, whose criteria
include problem solving ability and relevance by demonstrating its *use *in
modelling systems. What is not
acceptable is to fail to demonstrate that it succeeds by any kind of
criteria. Some of the formalist papers
in MAS fail in precisely this way, they excuse themselves of solving particular
problems but also fail to exhibit and substantial theorems and proofs.

Some Suggestions for the Way Forward

It should be clear that I am
not against the use of formal logics as a tool for understanding MAS *per se*,
but against using them in unhelpful ways, namely as a language for
philosophical discussion. Intuitions
that are relatively unconstrained and unvalidated have a poor track-record when
it comes to real applications and problems, and formalising these in relatively
simple (and, I argued, inappropriate) logics does nothing to solve this basic
problem. Simply following the form of a
philosophical tradition is insufficient to justify the presentation of work –
an audience rightly expects some conclusions in the form of results by which
they can evaluate the ideas. Yet we do
need somewhat abstract and precise models to improve our understanding, and
logics are an expressive and flexible kind of formal system. So might be the way forward?

Before suggesting some
steps we might take, I will describe our domain as I guess it is. I think that the study of social systems in
general, and MAS in particular, will be more akin to biology than to physics
and the production of MAS closer to stock breeding and ecological management
than to traditional engineering^{[6]}. I
think that there will be hundreds of essentially different ‘species’ of MAS,
all of which will need to be individually described studied rather than their
being adequately covered by any easily accessible universal principles^{[7]}. I
think that there will not be any easy ‘short cut’ to useful high theory, and
certainly not via vague intuitions expressed in formal logic. Thus I would the
following based upon analogies with other sciences:

· The development of new ways of collecting data and observing MAS;

· A considerable period of descriptive modelling (i.e. less abstract modelling) so that we have a way to compare different MAS;

· A building up of complete chains made up of models at different levels of abstraction so that each are each clearly related (or relatable) to less abstract models;

· The insistence that any abstract or formal theory is treated with scepticism until it proves its worth – the more abstract it is the more is has to prove;

· That, nonetheless, we continue to try to build models whose level of abstraction is justified by (and judged by) the evidence;

· The rejection of papers that merely specify things based on single cases, intuitions and expressiveness because they are premature;

· That, nonetheless, the greatest variety of formal systems should be encouraged as possible members of a ‘tool box’ for MAS practioners and studiers (but only accepted after they have shown to be helpful in at least one real case).;

· That papers suggesting formal systems for helping design MAS should demonstrate that it is feasible to design an MAS that works using them;

· That papers suggesting formal systems for understanding MAS should show that they do, in fact, capture the phenomena they claim providing either a successful prediction or a credible explanation of that phenomena;

· That the field resists the temptation to retreat into formalism and philosophy when it substantial progress is difficult.

This is a more *pragmatic* and less ambitious approach than many
academics have hoped for or will accept.
They will continue to dream of inventing the ‘magic bullet’ that allows
us to shortcut the large amount of messy empirical work that will be necessary
and take us straight to powerful high theory (as, indeed, do I in moments of
weakness). However I think this has
more chance of producing useful knowledge and, *eventually*, useful
theory. We will always continue to need
some sort of abstractions to help us search, but until we have some well validated
examples we need to stay as flexible as possible and stay suspicious of easy or
prevalent intuitions.

A Concluding Exercise

Look through some of the
papers in this (and similar) volumes.
Does the ‘conclusion’ state what was done and why it was done but not
state any results or conclusions (other than that the authors think it is the
right way to do it)? Is there any way
of *evaluating *what was done using the information in the paper? Is there any way of knowing when the
techniques or ideas described in the paper would be useful to apply and when
not? Have you been informed of anything
except the present state of thought of the authors? If there were no results, did the system (either formal or
software) help demonstrate or communicate the authors ideas effectively? Where those ideas so good to warrant
presentation with no results?

One way of stripping bare the impressive effect that a formal logic imparts is to imagine the same sort of paper but using a simulation instead of a logic. If the paper was one where a simulation was described along with the reasons why it was so designed, but the simulation was not actually run and no results were shown, would it make a satisfactory paper? I think not.

References

Conte, R.,
Edmonds, B., Moss, S. and Sawyer, R. K. (2001). Sociology and Social Theory in
Agent Based Social Simulation: A Symposium. *Computational and Mathematical
Organization Theory*, **7**:183-205.

Edmonds, B. (2000) The Purpose and Place of Formal Systems in the Development of Science, CPM Report 00-75, MMU, UK. http://cfpm.org/cpmrep75.html

Edmonds, B. (2002)
*Simplicity is Not Truth-Indicative*. CPM Report 02-00, MMU, 2002. http://cfpm.org/cpmrep99.html

Gabbay, D. M.
(1993) *Classical vs. non-classical logics : the universality of classic
logic*. Saarbrücken : Max-Planck-Instituit für Informatik.

Gabbay, D. M.
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^{[1]} As David Hales would say.

^{[2]}http://sdml.cfpm.org

^{[3]} Although this still leaves question of the appropriateness of the
implicit bias of the system.

^{[4]} For a thorough discussion of the nature of logic see (Gabbay 1994).

^{[5]} I know of no attempts to justify such an assumption, rather the
development of such logical formalisms seems to be on the basis that *any*
caputuring of such mental entities is impressive and hence interesting, so it
is felt that simple plausibility is sufficient to justify such explorations.

^{[6]} Or, at least, to a traditional account of what traditional
engineers do. Engineers, in practice, don’t actually act as these accounts
would suggest. A classic example of
this is the neatly ordered elicit; analyse; design; implement; test cycle that
software engineers are supposed to follow.

^{[7]} After all a 2D cellural automata with extremely simple rules for
each node can implement a full Turing machine and hence, in principle, *any*
computation.