Introduction

Philosophers constantly debate the nature of their discipline. These interminable debates frustrate even the most patient observer. Workers in AI also disagree, although not so frequently, about how to conduct their research. To equate programs with theories may offer a simple unifying tool to achieve agreement about the proper AI methodology. To construct a program becomes a way to construct a theory. When AI researchers need to justify their product as scientific, they can simply point to their successful programs. Unfortunately, methodological agreement does not come so easily in AI.

For a number of reasons, theorists in any discipline do not relish washing their proverbially dirty laundry in public. Methodology creates a great deal of that dirt, and philosophy of science supposedly supplies the soap to cleanse the discipline's methodology. Scientists often appeal to philosophers of science to develop methodological canons. It certainly does not instill confidence in a discipline if its practitioners cannot even agree on how to evaluate each other's work. Despite public images to the contrary, disagreements over how to approach a subject matter predominate in most scientific disciplines. Can philosophy of science come to the rescue of AI methodology? Yes and no.

Before describing the middle ground occupied by philosophy of science in its relationship to AI, we need to examine how some dismiss the AI research project altogether. In a previous article I argued against the various philosophical obstacles to the program/theory equation (Simon, 1979). I considered three types of objections to AI research: impossibility, ethical, and implausibility.

Introduction

The area of non-monotonic reasoning and the area of logic programming are of crucial and growing significance to artificial intelligence and to the whole field of computer science. It is therefore important to achieve a better understanding of the relationship existing between these two fields.

The major goal in the area of non-monotonic reasoning is to find adequate and sufficiently powerful formalizations of various types of non-monotonic reasoning – including common-sense reasoning – and to develop efficient ways of their implementation. Most of the currently existing formalizations are based on mathematical logic.

Logic programming introduced to computer science the important concept of declarative – as opposed to procedural – programming, based on mathematical logic. Logic programs, however, do not use logical negation, but instead rely on a non-monotonic operator – often referred to as negation as failure – which represents a procedural form of negation.

Non-monotonic reasoning and logic programming are closely related. The importance of logic programming to the area of non-monotontic reasoning follows from the fact that, as observed by several researchers (see e.g. Reiter, [to appear]) the non-monotonic character of procedural negation used in logic programming often makes it possible to efficiently implement other non-monotonic formalisms in Prolog or in other logic programming languages. Logic programming can also be used to provide formalizations for special forms of non-monotonic reasoning. For example, Kowalski and Sergot's calculus of events (1986) uses Prolog's negation-asfailure operator to formalize the temporal persistence problem in AI.

Fodor restates his language of thought hypothesis, which presents a serious challenge to the view that the architecture of cognition is network-based. Fodor claims that, whatever the representation underlying thought at the level of semantic interpretation, it must have constituent structure, i.e. a structure such that belief in the truth of (A and B) necessarily involves belief in the truth of both of the constituents, A and B, separately. Such necessity is not, in general, supported by network architecture whereas it is in Turing machine-type representations.

The rest of the papers in this section respond (directly or indirectly) to this challenge to the significance of connectionism in AI. Is connectionism just implementation detail, an essentially Turing machine-type architecture implemented with an activity-passing network? Or are sub-symbolic networks inherently more powerful than the traditional symbolic-level processing representations that have dominated much of AI? Smolensky is firmly on the side of connectionism as a fundamentally new and powerful ‘sub-symbolic’ paradigm for AI. Wilks discusses and denies the central claims of both Fodor and Smolensky, arguing that, at the moment, benificent agnosticism is the best position on connectionism, awaiting further clarification of its claims and more empirical results.

Churchland supports the connectionist movement but his support is based on the similarities between connectionist principles and the architecture of the brain. He argues for the study of neuroanatomy as a source of system-building constraints in AI.

Prolegomenon

My concern is with what an AI experiment is, and hence with what AI is. I shall talk about what experiments are actually like, but suggest that this is what they must be like.

Thus is it reasonable to suppose that AI experiments are, or could be, like the experiments of classical physics? I do not believe it is. This is not because we cannot expect the result of a single critical experiment to validate a theory, as we cannot expect a single translation to validate a translation program, for example: we can presumably extend the classical model to cover the case where validation depends on a set of results, for different data. Nor is it because we have not in practice got anything like an adequate predictive theory. I believe that we cannot in principle have the sort of predictive theory associated with physics, because we are not modelling nature in the classical physics sense. I shall elaborate on what I think we are doing, but claim now that we reach the same conclusion if we consider the suggestion that we are not in the classical physics position, but rather in that of investigative biologists, doing experiments to find out what nature is like (notionally without any theory at all, though perhaps in fact influenced by some half-baked theory). This is because there is nothing natural to discover.

Artificial intelligence is a subject that, due to the massive, often quite unintelligible, publicity that it gets, is nearly completely misunderstood by people outside the field. Even AIs practitioners are somewhat confused with respect to what AI is really about.

Is AI mathematics? A great many AI researchers believe strongly that knowledge representations used in AI programs must conform to previously established formalisms and logics or else the field will be unprincipled and ad hoc. Many AI researchers believe that they know how the answer will turn out before they have figured out what exactly the questions are. They know that some mathematical formalism or other must be the best way to express the contents of the knowledge that people have. Thus, to them, AI is an exercise in the search for the proper formalisms to use in representing knowledge.

Is AI software engineering? A great many AI practitioners seem to think so. If you can put knowledge into a program, then that program must be an AI program. This conception of AI, derived as it is from much of the work going on in industry in expert systems, has served to confuse AI people tremendously about what the correct focus of AI ought to be, and about what the fundamental issues in AI are.

A psychologist of my acquaintance, neither unaware of nor unsympathetic to work influenced by AI, recently referred to computational psychology as ‘very specialized’. Is this a fair assessment? Is Al-based psychology a mere hidden backwater, separated from the psychological mainstream? Sociologically, it must be admitted that it is. But theoretically? Perhaps the backwater is where the action is (and so much the worse for those who cannot see it)? Could it become the mainstream itself? In short, has AI helped psychology, or has it failed to live up to its early promise?

AI has undoubtedly helped psychology in some, very general, ways. It has provided a standard of rigour and completeness to which theoretical explanations should aspire (which is not to say that a program is in itself a theory). It has highlighted the importance of asking detailed questions about mental processes – about not just what the mind does, but how. It has alerted theoretical psychologists to the enormous richness and computational power of the mind. And it has furthered our understanding of how psychological, intentional, phenomena are possible in a basically material universe. If only for these reasons, AI has already been of lasting benefit to psychology. Certain sorts of theoretical inadequacies should be less common in the future than in the past.

From the beginning of computing people have been trying to make computers do more and more difficult things. At first these things were difficult in the sense that people could do them but rather tediously and unreliably, like solving lots of simultaneous equations. Then they were things that for practical purposes people could not do at all, like the calculations of theoretical chemistry. Progress was made by:

Researchers were slightly surprised to find that, when they wanted computers to do things that people find relatively easy, progress was much more difficult. This should perhaps be rephrased a bit. After all, people do not pick up objects in a three-pronged steel gripper, and they do not translate from French to English starting with the text punched on cards. Nor do they see through television cameras or hear through microphones. It was hard to progress with problems that looked as if they were in all material respects like things that people can do fairly easily.

Goldsmith's rustics were quite right about the village schoolmaster, of course, well in advance of their time and, apparently, of Goldsmith. But perhaps the time has come for less of such gazing, by AI researchers in particular, and more attention to their proper business. I am sure, for reasons I shall try to make clear, that the present situation, where much new work in AI is immediately proposed as new ‘model of the human brain or behaviour’, is an undesirable one.

This is a philosophical discussion about AI rather than a practical one; and intended to remind some AI researchers of standard uses of the words ‘model’ and ‘theory’ that they may have forgotten, and to explore some of the terminological consequences of a less liberal approach to these words than is the current fashion within AI.

Since it is a philosophical discussion, it is not intended to criticize any form of activity, or to suggest that it should not be carried out. It is concerned with how such work should be described, in the sense of what its ultimate subject matter is, and that such descriptions should be both revealing and consistent, and above all not misleading. I take it for granted in what follows that such questions are not “mere matters of words” or convention, and that it is no defence at any point to say that one can use the words ‘theory’ and ‘model’ to mean whatever one chooses.

In addition to the various edited collections and single-author volumes that concentrate on the philosophical foundations of AI, there is a recent collected volume that is devoted to the formal foundations of AI (Genesereth and Nilsson, 1987). The existence of this specific work relieves us of the necessity of devoting a large number of pages in the present collection to this important foundational aspect of AI. Nevertheless, for the sake of completeness and in order to provide a natural focus for the papers that do consider formal foundational issues, we decided to include the current chapter.

In the previous section Chandrasekaran introduced and discussed the role and flavour of logical abstraction theories in AI. Logical formalisms have always been favored as the best candidates with which to construct a science of AI, and notable successes can be found: McCarthy's LISP, the basic language of AI, based on the lambda calculus, and PROLOG, a language now inextricably intertwined with expert systems' technology. The latter became a practical possibility with the discovery of linear-time algorithms based on Robinson's resolution principle for mechanical proof. Another AI sub-area in which formal results have been obtained is heuristic and non-heuristic search: efficient searching of a large space of possibilities is seen by many to be a paradigm with general applicability in AI, and definite progress has been made with the formal characterization of the problem.

This book collects together a group of fundamental papers on the foundations of artificial intelligence, with selected papers and subsequent discussion from a workshop on the foundations of AI held in Las Cruces, New Mexico, in 1986. The liveliness of the workshop papers and discussions is intended to complement the older, classic papers.

To give the book a structure that will make it accessible to students of the field, we have added a full annotated bibliography, as well as binding explanatory material between the contributions.

At the Las Cruces workshop one of the first questions confronted was the role played by philosophy in the foundations of AI, since philosophy is a subject that comes running whenever foundational or methodological issues arise. The question is important and inevitable but it must always be remembered that there is still an unreformed core of AI practitioners who believe that such assistance – not only from philosophers but from psychologists and linguists as well – can only detract from serious methodological discussions that should take place only between practitioners in private. (A distinguished AI figure said this during the planning period for the workshop.) We need to ask whether that attitude is normal in the sciences, or would-be sciences. For, if it is, then AI is in no way special in these matters, and we can draw benefit from study of the methodologies of other sciences.

Artificial Intelligence is a methodological mess: a surfeit of programs and a dearth of justified theories and principles. Typically we have a large and complex program that exhibits some interesting behaviours. The underlying principles are anybody's guess.

In addition, if principles are presented, the gulf between program and principle is sufficient to preclude any systematic discussion of the program-principle relationship. We must do more than just present a principle.

A methodology for abstracting and justifying the principles that underlie an AI program is explained and demonstrated. The viewpoint taken is that we cannot prove that a program embodies a given principle; we can only make a claim to this effect with an explicit supporting argument, and thereby provide a concrete basis for discussion of the credibility of the putative principle.

Introduction

AI is largely a behavioural science: a science that is founded upon the behaviour of programs. The working program embodies the theory or set of principles.

Computer programs are very persuasive arguments for the theory that they model. They are also largely incomprehensible to anyone but (or including?) their author. Hence whilst the credibility of the theory is founded on the program the theory, presented perhaps in terms of principles, is necessarily couched in the vagaries and generalizations of the English language; the relationship between the working program and the comprehensible principles can only be founded on faith. We need something better than this.

One of the important complexities that confounds many discussions of AI is its claims to be a science, and the significance of AI programs is that the constituent phenomena can be represented, explored, refuted, and supported, etc. at many different, but not obviously separable, levels. Is theorizing in AI carried forward primarily by building and observing the behavior of models, or should we have a complete, formal specification prior to modeling, with the model providing merely an existence proof of practical viability? Advocates can be found for both sides of this methodological argument, which is taken up again, from other viewpoints, in subsequent sections.

Marr's paper argues for caution in “explaining” phenomena in terms of a working program (a Type 2 theory in Marr's terminology). This level of theory, embodying as it does a “mound of small administrative decisions that are inevitable whenever a concrete program is designed,” can all too easily obscure and hide some simple, abstract theory (a Type 1 theory) that may underlie it. He concludes that exploration at the program level should continue, but we must be careful not to overvalue results at this methodological level: “in the present state of the art [in AI], it seems wiser to concentrate on problems that probably have Type 1 solutions, rather than on those that are almost certainly of Type 2.” Marr, like Hoare and Dijkstra (see Partridge and Wilks paper in section 10), is suggesting that we limit AI research, initially at least.

Introduction: Kuhnian paradigms in AI

Is it helpful or revealing to see the state of AI in, perhaps over-fashionable, Kuhnian (Kuhn, 1962) terms? In the Kuhnian view of things, scientific progress comes from social crisis: there are pre-paradigm sciences struggling to develop to the state of “normal science” in which routine experiments are done within an overarching theory that satisfies its adherents, and without daily worry about the adequacy of the theory.

At the same time, there will be other scientific theories under threat, whose theory is under pressure from either discontinuing instances or fundamental doubts about its foundations. In these situations, normal science can continue if the minds of adherents to the theory are closed to possible falsification until some irresistible falsifying circumstances arise, by accretion or by the discovery of a phenomenon that can no longer be ignored.

There is much that is circular in this (the notion of “irresistible,” for example) and there may be doubts as to whether AI is fundamentally science or engineering (we return to this below). But we may assume, for simplicity, that even if AI were engineering, similar social descriptions of its progress might apply (see Duffy, 1984).

Does AI show any of the signs of normality or crisis that would put it under one of those Kuhnian descriptions, and what would follow if that were so? It is easy to find normality: the production of certain kinds of elementary expert system (ES) within commercial software houses and other companies.

Introduction

Following the advice of the philosopher Karl Popper to remember that science is about problems and their solutions I expected each paper on the American Association for AFs 1982 conference (AAAI 82) held in Pittsburgh to contain two main parts: (a) the problem attacked, and (b) its proposed solution. In fact, almost no speaker stated an information-processing problem, and even fewer proposed solutions to one. The problems I want to address here are “What is an information processing problem?” and “If AI speakers do not present solutions to such problems, what do they, in fact, do?” The proposed solutions are presented forthwith.

Information processing problems

What kind of problems does AI research solve? The answer may seem self-evident: “How to program a computer to do X?”, where X is medical diagnosis, natural-language understanding, etc. But such questions will soon be of very little interest. In a few decades' time, any school teacher will be able to make a computer do amazing things, without any knowledge of computer science. If you doubt this, then you have not imagined an instructable production system with a sophisticated natural-language interface, running on a descendant of the Cray supercomputer. In fact, the schoolteacher is likely to find it easier to instruct the computer.

The foundational problem of the semantics of mental representation has been perhaps the primary topic of philosophical research in cognitive science in recent years, but progress has been negligible, largely because the philosophers have failed to acknowledge a major but entirely tacit difference of outlook that separates them into two schools of thought. My task here is to bring this central issue into the light.

The Great Divide I want to display resists a simple, straightforward formulation, not surprisingly, but we can locate it by retracing the steps of my exploration, which began with a discovery about some theorists' attitudes towards the interpretation of artifacts. The scales fell from my eyes during a discussion with Jerry Fodor and some other philosophers about a draft of a chapter of Fodor's Psychosemantics (Fodor, 1987). The chapter in question, “Meaning and the World Order,” concerns Fred Dretske's attempts (1981, especially chapter 8; 1985; 1986) to solve the problem of misrepresentation. As an aid to understanding the issue, I had proposed to Fodor and the other participants in the discussion that we first discuss a dead simple case of misrepresentation: a coin-slot testing apparatus on a vending machine accepting a slug. “That sort of case is irrelevant,” Fodor retorted instantly, “because after all, John Searle is right about one thing; he's right about artifacts like that. They don't have any intrinsic or original intentionality – only derived intentionality.”

Artificial intelligence is the study of complex information-processing problems that often have their roots in some aspect of biological information processing. The goal of the subject is to identify interesting and solvable information-processing problems, and solve them.

The solution to an information-processing problem divides naturally into two parts. In the first, the underlying nature of a particular computation is characterized, and its basis in the physical world is understood. One can think of this part as an abstract formulation of what is being computed and why, and I shall refer to it as the “theory” of a computation. The second part consists of particular algorithms for implementing a computation, and so it specifies how. The choice of algorithm usually depends upon the hardware in which the process is to run, and there may be many algorithms that implement the same computation. The theory of a computation, on the other hand, depends only on the nature of the problem to which it is a solution. Jardine and Sibson (1971) decomposed the subject of cluster analysis in precisely this way, using the term “method” to denote what I call the theory of a computation.

To make the distinction clear, let us take the case of Fourier analysis. The (computational) theory of the Fourier transform is well understood, and is expressed independently of the particular way in which it is computed. There are, however, several algorithms for implementing a Fourier transform – the Fast Fourier transform (Cooley and Tukey, 1965), which is a serial algorithm, and the parallel “spatial” algorithms that are based on the mechanisms of coherent optics.

The opening section presents two very different types of attempt to provide a general characterization of AI. For Schank, AI is a distributed phenomenon: ‘potentially … the algorithmic study of processes in every field of enquiry.’ In the absence of a definition, he characterizes AI in terms of a list of features that he considers to be critical. He argues that the the bifurcation of AI into a scientific and an applications track is so decisive that ‘the two routes have nothing to do with each other.’ Finally, he lists and briefly discusses ten problem areas in AI that will not admit of solutions in the foreseeable future.

Chandrasekaran's paper lays out in historical perspective the methodological paradigms within which AI projects and explorations have at different times, and in different places, been pursued.

He takes the opening shots at connectionism and the echoes continue throughout this book culminating in the papers of section 9. He also introduces the ‘symbolic’ paradigm (another recurring theme) and attempts to clarify the issue of ‘symbolic’ and ‘non-symbolic’ representations. He offers the ‘information processing level of abstraction’ as a unifying paradigm.

He presents and discusses, with the aid of representative examples, three classes of theories in AI: architectural theories, logical abstraction theories, and general functional theories of intelligence. The paper concludes with a clear preference for the last class of theories and offers a specific functionaltheory- type proposal about the nature of intelligence.

Within the discussion of the class of logic-based theories in AI, Chandrasekaran provides an overview and introduction to this important facet of the foundations of AI – the one that we deal with explicitly in the next chapter.

Introduction

The title of this paper contains both the words “mechanized” and “theory.” I want to make the point that the ideas presented here are not only of interest to theoreticians. I believe that any theory of interest to artificial intelligence must be realizable on a computer.

I am going to describe a working computer program, FOL, that embodies the mechanization of the ideas of logicians about theories of reasoning. This system converses with users in some first-order language. I will also explain how to build a new structure in which theory and metatheory interact in a particularly natural way. This structure has the additional property that it can be designed to reason about itself. This kind of self-reflexive logical structure is new and discussion of the full extent of its power will appear in another paper.

The purpose of this paper is to set down the main ideas underlying the system. Each example in this paper was chosen to illustrate an idea and each idea is developed by showing how the corresponding FOL feature works. I will not present difficult examples. More extensive examples and discussions of the limits of these features will be described in other places. The real power of this theory (and FOL) comes from an understanding of the interaction of these separate features. This means that after this paper is read it still requires some work to see how all of these features can be used. Complex examples will only confuse the issues at this point. Before these can be explained, the logical system must be fully understood.