Contains research objectives and reports on five research projects.Computation Center, M.I.T

Abrahams, P. W.

Bobrow, D. G.

Brayton, R. K.

Edwards, D. J.

Fox, Phyllis

Hodes, L.

Luckham, D. C.

McCarthy, J. J.

Minsky, M. L.

Park, D. M. R.

Russell, S. R.

Shannon, C. E.

Slagle, J. R.

Webber, M. B.

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XV. ARTIFICIAL INTELLIGENCE*Prof. J. McCarthy D. G. Bobrow D. C. LuckhamProf. M. L. Minsky R. K. Brayton D. M. R. ParkProf. C. E. Shannon D. J. Edwards S. R. RussellDr. Phyllis Fox L. Hodes J. R. SlagleP. W. Abrahams M. B. WebberRESEARCH OBJECTIVESThe purpose of our work is to investigate ways of making machines solve problemsthat are usually considered to require intelligence. Our procedure is to attack the prob-lems by programming a computer to deal directly with the necessary abstractions,rather than by simulating hypothetical physiological structures. When a method forsolving a problem is not known, searches over spaces of potential solutions of the prob-lem, or of parts of the problem, are necessary. The space of potential solutions ofinteresting problems is ordinarily so enormous that it is necessary to devise heuristicmethods (1) to replace the searching of this space by a hierarchy of searches over sim-pler spaces. The major difficulty, at present, is the excessive length of time requiredfor building machinery or even for writing programs to test heuristic procedures. Forthis reason, the major part of our effort is going into the development of ways of com-municating with a computer more effectively than we can now. This work has twoaspects: a system for instructing the computer in declarative, as well as imperative,sentences, called the advice taker (2), and a programming language (3) for manipulatingsymbolic expressions that will be used for programming the advice-taker system andwill also be of more general use.J. McCarthy, M. L. MinskyReferences1. M. L. Minsky, Some methods of artificial intelligence and heuristic program-ming, a paper presented at the Symposium on the Mechanization of Thought Processes,National Physical Laboratory, Teddington, England, Nov. 24-27, 1958.2. J. McCarthy, Programs with common sense, a paper presented at the Symposiumon the Mechanization of Thought Processes, National Physical Laboratory, Teddington,England, Nov. 24-27, 1958.3. J. McCarthy, Recursive functions of symbolic expressions, Quarterly ProgressReport No. 53, Research Laboratory of Electronics, M.I.T., April 15, 1959,pp. 124-152.A. THE LISP PROGRAMMING SYSTEMThe LISP programming system is being improved in a number of ways.(a) Brayton and Park are finishing the LISP compiler and are attaching it to thesystem. Already, a compiled program has completed in 0.6 minute a calculation thatwas not completed in 30 minutes in the interpretive mode.This work is supported jointly by Research Laboratory of Electronics and theComputation Center, M.I.T.158(XV. ARTIFICIAL INTELLIGENCE)(b) Luckham and Edwards are finishing the necessary programs so that LISPprograms can be operated from the flexo-writer, and share time with the M.I.T. opera-tor program. Experiments have indicated that progress in checking out programs willbe much faster, once we can work on-line.(c) Fox is writing a programmer's manual for the LISP system.(d) Experience with the present LISP system on a number of small problems hasshown the importance of being able to compute with other quantities than symbolicexpressions, and a revised version of LISP is being considered which will allow compu-tation of recursive functions of a wide variety of kinds of information.B. THE ADVICE TAKERMinsky and Russell have begun programming a version of the Advice Taker, startingwith routines for achieving goals that may involve establishing structures of subgoals.C. THEORY OF COMPUTATIONThe recursive function formalism as developed for LISP, described in QuarterlyProgress Report No. 53, pages 124-151, has led to considerable simplification andclarification in the descriptions of algorithms. It now seems feasible to develop a logi-cal system in which proofs of the properties of computations can be put into a machine-checkable form with little more work than is involved in an informal argument, andindeed, sometimes, with less work. We hope this will eventually make it possible toeliminate debugging, that is, the trial of programs on repeated test cases, by making itpossible to prove that a program has desired properties and checking the proof on amachine.The insight into the nature of computational processes that is being gained will helpwith the artificial intelligence problem because in present attempts to make machinesimprove their own programs most of the effort is spent fighting the language in whichthe programs are described.Some of the results of this theory are the following:(a) The conditional expression and recursive function formalism described inQuarterly Progress Report No. 53 allows us to define the class C{3} of functionscomputable in terms of the functions of a base class F. Adding quantifiers and adescription operator allows the definition of A{9}, the class of functions arithmeticover F.(b) A formal method of proof called "recursion induction" makes proofs of thesimpler properties of recursive functions entirely mechanical. For example, considerthe recursive function159(XV. ARTIFICIAL INTELLIGENCE)f(n, m, p) = (m=n-.p, T-f(n, m+ 1, (m+ 1)p))It is desired to prove that f(n, m, p) = !p. The method of recursion induction allowsus to assume the result for the occurrences of the function on the right. Thus we havef(n, m, p) = m=n ! p, T- ! (m+ 1)pM! (m+ 1) .=m=n!- p, T-nI )n!m!which allows us to conclude that the formula holds for all n, m, p for which the compu-tation terminates. A general form of recursion induction has been proved to be valid.(c) A formalism for the recursive definition of sets has been developed. Considera set S defined recursively byS = AU(SxS)where U stands for union, and x for Cartesian product. If A is the set of atomicsymbols, S is the set of S-expressions. As another example, the set I defined byI = {o} U ({o}xl)where {o} is the set whose sole member is o, may be regarded as the set of non-negative integers, and the operations on integers are definable in terms of the canonicalprojection and injection mappings associated with the definition.(d) Considerable progress has been made in devising a formalism whereby proofsthat are checkable by computer can be easily written. When proofs are written to beread by a person the style chosen is a compromise between what is easy for the writerto write and for the reader to follow. If proofs are to be checked by machine, we canmake things easier for the writer by taking advantage of the machine's ability to verifythe assertion that a given calculation has a given result, regardless of how complicatedthe calculation is. We accomplish this by formalizing metasyntax so that a procedurefor generating a proof is acceptable as a metaproof. Whatever the base system, themetasystem contains recursive functions of symbolic expressions so that any proof-generation procedure is expressible.(e) Park has written LISP programs to simplify conditional expressions, andAbrahams is programming part of the metamathematical procedure.(f) A full report of the work on the theory of computation is being prepared.D. CHESSThe chess program has been taken over by a syndicate of sophomores.160(XV. ARTIFICIAL INTELLIGENCE)E. INTEGRATIONSlagle's integration program has solved some simple problems, and it is beingextended.J. McCarthy161

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