By Morris Rubinoff, Marshall C. Yovits

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Extra info for Advances in Computers, Vol. 15

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A short, somewhat oversimplified discussion of resolution theorem proving will be included here and the reader is referred to Chang and Lee (1973) , Nilsson (1971) , and Slagle (1971) for additional details. In resolution theorem proving, all axioms and theorems are converted to clause form, a set of predicates in disjunctive form with all universal and existential quantifiers removed. That is, any well-formed formula can be converted V P,,where each Pi is a to a set of clauses of the form PI V P2 V PI V (possibly negated) predicate symbol with zero or more arguments, which may or may not be instantiated.

The only way this strategy can be made to work is to enumerate a subset of the partial recursive functions for which the halting problem is solvable or to allow for a partial solution to the halting problem by limiting the number of steps a program may complete before it halts. These theoretical issues and others are discussed at length in Biermann and Feldman (1972), Barzdin and Freivald (1972), Blum and Blum (1975) ,Feldman (1972b), Gold (1967) , and Solomonoff (1964). Suppose the solution by enumeration method can be made to work by one of the above techniques.

U. Why did you clean off that cube? A. TO PUT IT ON A LARGE GREEN CUBE. U. Why did you do that? A. TO STACK UP THE RED CUBE, A LARGE RED BLOCK, AND A LARGE GREEN ONE. U. Why did you do that? A. BECAUSE YOU ASKED ME TO. U. How did you do it? A. BY PUTTING A LARGE RED BLOCK ON THE TABLE; THEN LETTING GO OF IT; THEN PUTTING.. . Finally, Winograd’s system can accept some kinds of declarative information. Such sentences result in new theorems or facts being stored into the system’s knowledge base as illustrated by the following sequence: U.

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