The formulation of the resolution principle by J. A. Robinson (1965a) has provided the impetus for a number of recent efforts in automatic theoremproving. These programs have generated proofs of some interesting propositions of number theory, in addition to theorems of first-order functional logic and group theory. A'literal' is an n-place predicate expression or its negation F(xi, x2,.-.., x) F(xi, x2,., x „) whose arguments are individual variables, individual constants, or functional expressions. Quantifiers do not occur in these formulae, since existentially quantified variables have been replaced by functions of universally quantified ones, and the remaining variables may therefore be taken as universally quantified. For example, the number-theoretic proposition'For all x and y, if x is a divisor of y then there exists some z such that x times z equals y' may be symbolised as D(x, y)v T(x, f(x, y), y) in which D(x, y)' stands for x is a divisor of y' and 7(x, y, z)' stands for'x times y equals z'.

Lisp, etc.) are designed for off-line use. With the above examples in mind, certain principles seem obvious. The online user can make best use of such a system by building up complex entities in small units. For example, when calculating a large expression, it is better to work out parts of it and store these parts in variables, rather than try to do the whole thing at once. In the above examples pop-1 has appeared as a language with a fixed vocabulary.

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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

PhD. dissertation, Harvard University, August 1967. Reprinted as a volume in the series Outstanding Dissertations in the Computer Sciences, New York: Garland Publishing, 1979

In Fox, L. (Ed.), Advances in Programming and Non-Numerical Computation, pp. 183–200. Pergamon.

Annals of Mathematical Statistics, 41.

In B. Kleinmuntz (Ed.), Problem solving. New York: Wiley, 51-119.

Operations Research 14:699-719

Research on question answering by Raphael, Black, and Elliott, and our own work on Protosynthex II has shown that question-answering algorithms can be most easily written if the text source is in the form of simple, explicitly structured sets of subject-verb-nominal strings. Question-answering algorithms that have thus far been developed include word- and structure-matching operations and some few logical inference functions. All of the systems cited have in some fashion limited their input language to simple subject-verb-nominal strings, thus eliminating many problems of syntactic analysis and providing a normalized form for language data.