Lattice-based paraconsistent logic

Abstract

In this paper we describe a procedure for developing models und associated proof systems for two styles of paraconsistent logic. We first give an Urquhart-style representation of bounded not necessarily discrete lattices using (grill, cogrill) pairs. From this we develop Kripke semantics for a logic permitting 3 truth values: true, false and both true and false, We then enrich the lattice by addeling a unary operation of negation that is involutive and aritimonotoue and show that the representation may be extended to those lattices. This yields Kripke semantics for a nonexplosive 3-valued logic with negation. © Springer-Verlag Berlin Heidelberg 2006.