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

BOXES is the name of a computer program. This is what the chess player does when he lumps together large numbers of positions as being'similar' to each other, by neglecting the strategically irrelevant features in which they differ. The resultant small game can be said to be a'model' of the large game. To give a brutally extreme example, consider a specification of chess positions so incomplete as to map from the viewpoint of White the approximately 1050 positions of the large game on to the seven shown in Figure 1. Even this simple classification may have a role in the learning of chess.

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.

"The purpose of this paper is to clarify some basic issues of choice of representation for problems of reasoning about actions. The general problem of re- Presentation is concerned with the relationship between different ways of formulating a problem to a problem solving system and the efficiency with which the system can be expected to find a solution to the problem. An understanding of the relationship between problem formulation and problem solving efficiency is a prerequisite for the design of procedures that can automatically choose the most `appropriate' representation of a problem ( they can find a `point of view' of the problem that maximally simplifies the process of finding a solution).Many problems of practical importance are problems of reasoning about actions. In these problems, a course of action has to be found that satisfies a number of specified conditions. A formal definition of this class of problems is given in the next section, in the context of a general conceptual framework for formulating these problems for computers. Everyday examples of reasoning about actions include planning an airplane trip, organizing a dinner party, etc. There are many examples of industrial and military problems in this category, such as scheduling assembly and transportation processes, designing a program for a computer, planning a military operation, etc."In D.Michie (Ed.), Machine intelligence 3. New York: American Elsevier,131-171

Wiley is a global provider of content and content-enabled workflow solutions in areas of scientific, technical, medical, and scholarly research; professional development; and education. Our core businesses produce scientific, technical, medical, and scholarly journals, reference works, books, database services, and advertising; professional books, subscription products, certification and training services and online applications; and education content and services including integrated online teaching and learning resources for undergraduate and graduate students and lifelong learners. Founded in 1807, John Wiley & Sons, Inc. has been a valued source of information and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Wiley has published the works of more than 450 Nobel laureates in all categories: Literature, Economics, Physiology or Medicine, Physics, Chemistry, and Peace. Wiley has partnerships with many of the world's leading societies and publishes over 1,500 peer-reviewed journals and 1,500 new books annually in print and online, as well as databases, major reference works and laboratory protocols in STMS subjects.

Since mid-November 1966 a chess program has been under development at the Artificial Intelligence Laboratory of Project MAC at M.I.T. This paper describes the state of the program as of August 1967 and gives some of the details of the heuristics and algorithms employed.

A series of computer programs have been written to play the board game Go-Moku. Go-Moku is played on a 19 x 19 square mesh. Player b(w) has a supply of black (white) pieces. The players take it in turns to play a piece on a mesh point. The winner is the first player to complete a 5-pattern, that is, to make up a (horizontal, vertical or diagonal) line of five and only five adjacent pieces of his colour.

A new signature table technique is described together with an improved book learning procedure which is thought to be much superior to the linear polynomial method described earlier. Full use is made of the so called “alpha-beta” pruning and several forms of forward pruning to restrict the spread of the move tree and to permit the program to look ahead to a much greater depth than it other- wise could do. While still unable to outplay checker masters, the program’s playing ability has been greatly improved.See also:IEEE XploreAnnual Review in Automatic Programming, Volume 6, Part 1, 1969, Pages 1–36Some Studies in Machine Learning Using the Game of CheckersIBM J of Research and Development ll, No.6, 1967,601

This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review. This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only.

One of the fundamental concepts in mathematics is that of transformation. The study of the unfolding over time of a physical process leads naturally to investigations of the effects of the repetition of a transformation, which is to say to the study of multistage processes. Much of classical and contemporary analysis stems from this source: iteration, ergodic theory, the theory of semigroups [1], the theory of branching processes [2], random transformations at fixed times and deterministic transformations at stochastic times [3, 4]. We wish to indicate still another direction of research, that of multistage decision processes. What happens when we allow a choice of the transformation to be employed at each time?