On the logic of distributive nearlattices

Abstract

We study the propositional logic (Formula presented.) associated with the variety of distributive nearlattices (Formula presented.). We prove that the logic (Formula presented.) coincides with the assertional logic associated with the variety (Formula presented.) and with the order-based logic associated with (Formula presented.). We obtain a characterization of the reduced matrix models of logic (Formula presented.). We develop a connection between the logic (Formula presented.) and the (Formula presented.) -fragment of classical logic. Finally, we present two Hilbert-style axiomatizations for the logic (Formula presented.).