An efficient relational deductive system for propositional non-classical logics

Abstract

We describe a relational framework that uniformly supports formalization and automated reasoning in varied propositional modal logics. The proof system we propose is a relational variant of the classical Rasiowa-Sikorski proof system. We introduce a compact graph-based representation of formulae and proofs supporting an efficient implementation of the basic inference engine, as well as of a number of refinements. Completeness and soundness results are shown and a Prolog implementation is described.

Keywords:

• Rasiowa-Sikorski proof systems
• relational reasoning
• non-classical logics