The predicate elimination strategy in theorem proving

Authors:
Raymond Reiter
Affiliations:
Department of Computer Science, University of British Columbia, Vancouver 8, British Columbia
Venue:
STOC '70 Proceedings of the second annual ACM symposium on Theory of computing
Year:
1970

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Abstract

The predicate elimination strategy is a complete resolution proof strategy for multi-predicate formulas. Essentially, the procedure focuses on one of the predicate symbols P, and attempts to deduce clauses independent of P by means of resolution in which only predicates in P are “resolved away” from parent clauses. The completeness theorem states that one can in this way, deduce an unsatisfiable P-independent set of clauses, provided the given set is unsatisfiable. The strategy is then extended to a suitable form of semantic resolution. This leads to the following strategy: in the attempt to deduce an unsatisfiable P-independent set of clauses, apply elementary resolution to “resolve away” predicates in P only from parent clauses, one of which has all of its predicates in P positive (negative).