Automatic Theorem Proving With Renamable and Semantic Resolution

  • Authors:

  • James R. Slagle

  • Affiliations:

  • Lawrence Radiation Laboratory University of California, Livermore, California

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1967

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Abstract

The theory of J. A. Robinson's resolution principle, an inference rule for first-order predicate calculus, is unified and extended. A theorem-proving computer program based on the new theory is proposed and the proposed semantic resolution program is compared with hyper-resolution and set-of-support resolution programs. Renamable and semantic resolution are defined and shown to be identical. Given a model M, semantic resolution is the resolution of a latent clash in which each “electron” is at least sometimes false under M; the nucleus is at least sometimes true under M.The completeness theorem for semantic resolution and all previous completeness theorems for resolution (including ordinary, hyper-, and set-of-support resolution) can be derived from a slightly more general form of the following theorem. If U is a finite, truth-functionally unsatisfiable set of nonempty clauses and if M is a ground model, then there exists an unresolved maximal semantic clash [E1, E2, · · ·, Eq, C] with nucleus C such that any set containing C and one or more of the electrons E1, E2, · · ·, Eq is an unresolved semantic clash in U.