Spectral Duality for Finitely Generated Nilpotent Minimum Algebras, with Applications |
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| Authors: | Aguzzoli, Stefano Busaniche, Manuela Marra, Vincenzo |
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| Affiliation: | Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39–41, 20135 Milano, Italy. E-mail: aguzzoli{at}dsi.unimi.it |
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| Abstract: | We establish a categorical duality for the finitely generatedLindenbaum-Tarski algebras of propositional nilpotent minimumlogic. The latter's conjunction is semantically interpretedby a left-continuous (but not continuous) triangular norm; implicationis obtained through residuation. Our duality allows one to transferto nilpotent minimum logic several known results about inutitionisticlogic with the prelinearity axiom (also called Gödel-Dummettlogic), mutatis mutandis. We give several such applications. |
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| Keywords: | Spectral duality prime spectrum amalgamation interpolation t-norm based logics |
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