Using forcing to prove completeness of resolution and paramodulation

Authors:
John Pais;Gerald E. Peterson
Affiliations:
McDonnell Douglas Corporation, 225/105/2, Mailcode 106 5165, P.O. Box 516, St. Louis, Missouri 63166, USA;McDonnell Douglas Corporation, 225/105/2, Mailcode 106 5165, P.O. Box 516, St. Louis, Missouri 63166, USA
Venue:
Journal of Symbolic Computation
Year:
1991

Citing 6
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Abstract

A technique for establishing completeness results for theorem proving systems in first-order logic with equality is presented. This technique is an adaptation of model theoretic forcing, which was originally designed to provide a method for constructing models of certain first-order logical theories. Our method applies to term orderings which may have infinitely many infinite extents, but transfinite trees are not used. We illustrate this method by proving the completeness of resolution and paramodulation, and the completeness of a set of inference rules consisting of restrictive forms of resolution and paramodulation, simplification and deletion of subsumed clauses.