Spectral duality for finitely generated nilpotent minimum algebras, with applications

Abstract

We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of prepositional nilpotent minimum logic. The latter's conjunction is semantically interpreted by a left-continuous (but not continuous) triangular norm; implication is obtained through residuation. Our duality allows one to transfer to nilpotent minimum, logic several known results about inutitionistic logic with the prelinearity axiom (also called Gödel-Dummett logic), mutatis mutandis. We give several such applications.