Spectral Duality for Finitely Generated Nilpotent Minimum Algebras, with Applications
Stefano Aguzzoli, Manuela Busaniche, Vincenzo Marra · Journal of Logic and Computation · 2007
We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of propositional 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.