Priestley Duality for Paraconsistent Nelson’s Logic

Abstract

The variety of $${{\bf N4}^\perp}$$ -lattices provides an algebraic semantics for the logic $${{\bf N4}^\perp}$$ , a version of Nelson's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of $${{\bf N4}^\perp}$$ -lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.