Abstract
A new deduction rule is introduced to give streamlined treatment to relations of special importance in an automated theorem-proving system. This relation matching rule generalizes to an arbitrary binary relation the E-resolution and RUE-resolution rules for equality, and may operate within a nonclausal or clausal system. The new rule depends on an extension of the notion of polarity to apply to subterms as well as to subsentences, with respect to a given binary relation. It allows the system to draw a conclusion even if the unification algorithm fails to find a complete match, provided the polarities of the mismatched terms are auspicious. The rule allows us to eliminate troublesome axioms, such as transitivity and monotonicity, from the system; proofs are shorter and more comprehensible, and the search space is correspondingly deflated.
This is an abbreviated version of a part of the paper “Special Relations in Automated Deduction” that will appear in the Journal of the ACM (1985). Another part of that paper appears in the proceedings of the Twelfth International Colloquium on Automata, Languages, and Programming (ICALP), Nafplion, Greece (July 1985), Springer-Verlag, Lecture Notes in Computer Science (W. Brauer, ed.), Vol. 194, pp. 413–423.
This research was supported in part by the National Science Foundation under grants MCS-82-14523 and MCS-81-05565, by the Defense Advanced Research Projects Agency under contract AFOSR-81-0014, by the Office of Naval Research under contract N00014-84-C-0706, and by a contract from the International Business Machines Corporation.
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Manna, Z., Waldinger, R. (1985). Deduction with relation matching. In: Maheshwari, S.N. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1985. Lecture Notes in Computer Science, vol 206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16042-6_12
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DOI: https://doi.org/10.1007/3-540-16042-6_12
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