Uniform notation of tableau rules for multiple-valued logics

Abstract

A framework for axiomatizing arbitrary finitely valued logics with minimal overhead compared to the classical case is presented. The main idea is to work with tableaux using generalized signs, which makes it possible to express complex assertions regarding the possible truth values of a formula. The class of regular logical connectives which, together with a suitable restriction on queries (i.e. allowed signs) to the system, allow a uniform notation style representation of multiple-valued propositional and first-order logics is introduced. It has been demonstrated that various systems differing in their allowed classes of connectives and complexity, of rules may be formulated. This allows the use of tools and methods that are close to the ones used in classical logic, both on the theoretical (uniform notation in definitions and proofs) and practical (use of classical theorem provers with few modifications) sides.<>