A new methodology for developing deduction methods

Abstract

This paper explores the use of resolution as a meta-framework for developing various, different deduction calculi. In this work the focus is on developing deduction calculi for modal dynamic logics. Dynamic modal logics are PDL-like extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and Rasiowa-Sikorski systems can be developed and studied by using standard principles and methods of first-order theorem proving. The approach is based on the translation of reasoning problems in modal logic to first-order clausal form and using a suitable refinement of resolution to construct and mimic derivations of the desired proof method. The inference rules of the calculus can then be read off from the clausal form. We show how this approach can be used to generate new proof calculi and prove soundness, completeness and decidability results. This slightly unusual approach allows us to gain new insights and results for familiar and less familiar logics, for different proof methods, and compare them not only theoretically but also empirically in a uniform framework.