Resolution-based Theorem Proving for Many-valued Logics

Abstract

A general approach to automated theorem proving for all first-order finite-valued logics that can be defined truth-functionally is described. The suggested proof procedure proceeds in two, largely independent, steps. First, logic-specific translation calculi are used to generate clause forms for arbitrary formulas of a many-valued logic. The worst-case complexity of the translation rules is analysed in some detail. In the second step a simple resolution principle is applied to the logic-free clause form. Some refinements of this resolution rule are demonstrated to be refutationally complete by means of a generalized concept of semantic trees. An investigation of some important families of many-valued logics illustrates the concepts introduced by concrete examples.