The problem discussed in this paper, namely that of finding a function to satisfy a given argument-value table, is by no means new to computing science, or to mathematics. Thus, for example, the problem of fitting a curve to a set of points is a part of numerical analysis. However, I am concerned with finding a function over a non-metric space, and so my work is closer to that of Feldman et al. (1969) in what they call, 'grammatical inference' or to the automaton-synthesizing programs described by Fogel, Owens and Walsh (1966).

Grammars or syntax specifications address themselves to the characterisation in symbolic terms of the structure of complex expressions. Two types of expression of empirical interest have been studied: sentences in English and other'natural' languages, and programs written in some high-level procedural language like ALGOL. Expressions in these languages consist of sets of elements (words and characters) coordinated with one another according to the sensorily manifest relationship'alongside', more commonly termed'followed by'.

A robot, in order to act intelligently, must be able to reason from facts which its sensors detect to conclusions which govern its actions. This reasoning process is so central to human intelligence that it seems immediately relevant to the problems of robot design to consider its properties, how it might be analysed and imitated.

This paper is a survey and discussion of research work relevant to the task of constructing some kind of reasoning robot. The emphasis is entirely on the organization of the reasoning processes, in particular planning, rather than on hardware. In practice the reasoning would most probably be carried out within a digital computer. My objective is to clarify the relationship between some superficially rather disparate approaches to this task, and simultaneously to indicate what seem to be the key problem areas. No new experimental results are presented, but the approach to the subject which I have adopted is a consequence of earlier experimentation with a simple computer simulation of a robot (Doran 1968a, 1969).

A minimal:robot,Icnown as Freddy, has been constructed with the aim of connecting a usable device online to the Department's lc L 4130, under the Multi-Pop time-sharing system, and discovering the snags. (See figure 1). Various technical problems arise when such a device runs free. It is much easier to anchor it and allow it to push its world about. Our present world is a three-foot diameter sandwich of hardboard and polystyrene which is light and rigid.

A computer program capable of acting intelligently in the world must have a general representation of the world in terms of which its inputs are interpreted. Designing such a program requires commitments about what knowledge is and how it is obtained. Thus, some of the major traditional problems of philosophy arise in artificial intelligence. More specifically, we want a computer program that decides what to do by inferring in a formal language that a certain strategy will achieve its assigned goal. This requires formalizing concepts of causality, ability, and knowledge. Such formalisms are also considered in philosophical logic. The first part of the paper begins with a philosophical point of view that seems to arise naturally once we take seriously the idea of actually making an intelligent machine.

It seems most unlikely that one could in general write purely applicative Schonfmkel descriptions', like (5), of functions already known to one in some other form. Fortunately there is a general procedure -- the Schonfmkel procedure -- which, when applied to any expression written in the more intuitive lambda-calculus notation, will produce a correct translation of it into the Schonfinkel notation.

Institut Blaise Pascal, C.N.R.S., 23, Rue du Maroc, 75, Paris XIX, France We study some aspects of a general game-playing program. Such a program receives as data the rules of a game: an algorithm enumerating the moves and an algorithm indicating how to win. The program associates to each move the conditions necessary for this move to occur. It must find how to avoid a dangerous move. We describe the part of the program playing the combinatorial game in order to win: how it can find the moves which lead to victory and what are the only opponent's moves with which he does not lose. This program has been tried with various games: chess, tictac-too, etc. 1. INTRODUCTION My aim was to realize a program playing several games. The rules of the particular game which it must play are given as data. If we want to have a performing program, it must be capable of studying these rules.

Note: PDF of full volume downloadable by clicking on title above (26 MB). Selected individual chapters available from the links below. CONTENTSINTRODUCTION MATHEMATICAL FOUNDATIONS1 The morphology of prex—an essay in meta-algorithmics. J. LAS KS 32 Program schemata. M. S. PATE RSON 193 Language definition and compiler validation. J. J. FLORENTIN 334 Placing trees in lexicographic order. H. I.S COINS 43 THEOREM PROVING5 A new look at mathematics and its mechanization. B. M ELTZER 636 Some notes on resolution strategies. B. MELTZER 717 The generalized resolution principle. J. A. ROBINSON 778 Some tree-paring strategies for theorem proving. D.LUCKHAM 959 Automatic theorem proving with equality substitutions andmathematical induction. J. L. D ARLINGTON 113 MACHINE LEARNING AND HEURISTIC PROGRAMMING10 On representations of problems of reasoning about actions.S.AMAREL 13111 Descriptions. E.W.ELCOCK 17312 Kalah on Atlas. A.G.BELL 18113 Experiments with a pleasure-seeking automaton: J. E. DORAN 19514 Collective behaviour and control problems. V.I.VARSHAVSKY 217 MAN—MACHINE INTERACTION15 A comparison of heuristic, interactive, and unaided methods ofsolving a shortest-route problem. D.MICHIE, J. G. FLEMING andJ. V.OLDFIELD 24516 Interactive programming at Carnegie Tech. A.H.BOND 25717 Maintenance of large computer systems—the engineer's assistant.M.H.J.BAYLIS 269 COGNITIVE PROCESSES: METHODS AND MODELS18 The syntactic analysis of English by machine. J.P.THORNE,P.BRATLEY and H.DEWAR 28119 The adaptive memorization of sequences. H.C.LONOUETHIGGINSand A.ORTONY 311 PATTERN RECOGNITION20 An application of Graph Theory in pattern recognition.C.J.HILDITCH 325 PROBLEM-ORIENTED LANGUAGES21 Some semantics for data structures. D. PARK 35122 Writing search algorithms in functional form. R.M.BURSTALL 37323 Assertions: programs written without specifying unnecessaryorder. J.M.FOSTER 38724 The design philosophy of Pop-2. R.J.POPPLESTONE 393 INDEX 403 Machine Intelligence Workshop

Young animals play games in order to prepare themselves for the business of serious living, without getting hurt in the training period. Game-playing on computers serves a similar function. It can teach us something about the structure of thought processes and the theory of struggle and has the advantage over economic modelling that the rules and objectives are clear-cut. If the machine wins tournaments it must be a good player. The complexity and originality of a master chess player is perhaps greater than that of a professional economist. The chess player continually pits his wits against other players and the precision of the rules makes feasible a depth of thinking comparable to that in mathematics. No program has yet been written that plays chess of even good amateur standard. A really good chess program would be a breakthrough in work on machine intelligence, and would be a great encouragement to workers in other parts of this field and to those who sponsor such work. In criticism of the writing of a chess program, Macdonald (1950) quoted a remark to the effect that a machine for smoking tobacco could be built, but would serve no useful purpose. The irony is that smoking machines have since been built in order to help research on the medical effects of smoking. This does not prove that a chess program should be written, but suggests that the arguments against it might be shallow. Many branches of science, and of pure and applied mathematics, have started with a study of apparently frivolous things such as puzzles and games. It is pertinent to ask in what way a good chess program would take us beyond the draughts program of A. The answer is related to the much greater complication of chess, the much larger number of variations and possible positions. In fact, the number of possible chess positions is about the cube or fourth power of the number of possible draughts positions (see Appendix E). Samuel was able to make considerable use of the storage of thousands of positions that had occurred in the previous experience of the machine, and this led to a very useful increase in the depth of analysis of individual positions. The value of this device depends on the probability that, at any moment in the analysis, we run into a position that has already been analysed and stored. This applies more generally to the goals and subgoals that occur to the chess player. Thus there should be'specificallydirected' as well as'routinely-directed' analysis. Another important aspect of chess thinking, also required in most other problem-solving, is what de Groot (1946, 1965) calls'progressive deepening' of an analysis. Typically an analysis of a position by a human player does not simply follow a tree formation, but contains cycles in which a piece of analysis is retraced and improved.