"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

In Hart, J. and Takasu, S. (Eds.), Systems and Computer Science. University of Toronto Press

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 Quantifiers do not occur in these formulae, since existentially quantified variables have been replaced by functions of universally quantified ones, and the remaining variables may therefore be taken as universally quantified.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.

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

Operations Research 14:699-719

Republished as The Mathematical Foundations of Learning Machines, San Francisco: Morgan Kaufmann Publishers, 1990McGraw-Hill. Republished in 1990.

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