Partial Instantiation Methods for Inference in First-Order Logic

  • Authors:

  • J. N. Hooker;G. Rago;V. Chandru;A. Shrivastava

  • Affiliations:

  • Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.;Computer Science Department, University of Pisa, Corso Italia 40, 156125 Pisa, Italy;Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India 560 012;Sanchez Computer Associates, 37/2, 4th Main, Malleswaram, Bangalore, India 560 003

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2002

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Abstract

Satisfiability algorithms for propositional logic have improved enormously in recently years. This improvement increases the attractiveness of satisfiability methods for first-order logic that reduce the problem to a series of ground-level satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolution-based methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (1) extending it to logic with functions, (2) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (3) simplifying it to obtain further speedup. We provide a similar development for a “dual” partial instantiation approach defined by Hooker and suggest a primal–dual strategy. We prove correctness of the primal and dual algorithms for full first-order logic with functions, as well as termination on unsatisfiable formulas. We also report some preliminary computational results.