Strategies for resolution method in non-classical logics (Abstract)

Abstract

We present a general method for construction and completeness proof of the resolution-type calculi for non-classical systems including linear logic. This is an extension of the method introduced by Maslov [1] for classical predicate logic, which can be summarized as follows: A resolution derivation of the goal clause g from a list F of input clauses can be obtained as the result of deleting F from the Gentzen-type cut-free derivation of the sequent F =~ g. Immediate extension of resolution to non-classical predicate logics is difficult because skolemization is usually non-available. We use ideas of the author [2] and Zamov [3] that allow one to avoid skolemization. We describe and prove completeness of resolution strategies corresponding to Gentzen-type derivability, and of the structure-preserving transformation GR from Gentzen-type system into the corresponding resolution system. This allows to incorporate strategies known for Gentzen-type (tableau) system G into the resolution framework: first some strategy is proved to be complete for G, then operation GR transfers this result to resolution.