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The application of automated reasoning to questions in mathematics and logic

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Abstract

Sharply different from the well-known use of various computer programs for the numerical aspects of mathematics and logic is the newer and less familiar use of a program to address the logical reasoning aspects. In this article, we focus on such a program — the automated reasoning program OTTER — which is portable, available electronically by anonymous FTP, and usable on a wide variety of computers, even on personal computers. We discuss the types of assistance provided by OTTER, including proof finding, conjecture formulation, and object construction. With OTTER's assistance, we have answered a number of open questions taken from a variety of fields. We focus on such questions from combinatory logic, equivalential calculus, Robbins algebra, and finite semigroup theory. For those who enjoy a challenge, we also offer ten questions, including some that are still open, and an open question that eluded even Tarski.

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This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, US Department of Energy, under Contract W-31-109-Eng-38.

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Wos, L., McCune, W. The application of automated reasoning to questions in mathematics and logic. Ann Math Artif Intell 5, 321–369 (1992). https://doi.org/10.1007/BF01543481

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