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Shortest Single Axioms for the Equivalential Calculus with CD and RCD

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Abstract

The automated reasoning assistants Otter and Mace are applied to the following open problem in equivalential calculus: Which equivalential tautologies will serve as shortest single axioms with both condensed detachment and reversed condensed detachment as inference rules? Earlier uses of Otter are extended and executed systematically by using a generic driver program. The application of Mace to this problem required the development of new techniques. The 630 possibilities are described, and seven new shortest single axioms are presented. All but five of the remaining possibilities (up to duality) are shown to be too weak, and it is noted that the above results supersede in some respects the results of a similar unpublished paper.

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Authors and Affiliations

  1. Automated Reasoning Project, The Australian National University, Australia

    Kahlil Hodgson

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  1. Kahlil Hodgson
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Hodgson, K. Shortest Single Axioms for the Equivalential Calculus with CD and RCD. Journal of Automated Reasoning 20, 283–316 (1998). https://doi.org/10.1023/A:1005731217123

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