Spectral duality for finitely generated nilpotent minimum algebras, with applications

AGUZZOLI, STEFANO; BUSANICHE, MANUELA; MARRA, VINCENZO

JOURNAL OF LOGIC AND COMPUTATION

Oxford Press

Lugar: Oxford; Año: 2007 vol. 17 p. 749 - 765

0955-792X

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 Godel-Dummett logic), mutatis mutandis. We give several such applications. 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 Godel-Dummett logic), mutatis mutandis. We give several such applications.mutatis mutandis. We give several such applications.