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Journal of Logic and Computation Advance Access originally published online on June 4, 2007
Journal of Logic and Computation 2007 17(4):749-765; doi:10.1093/logcom/exm021
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Spectral Duality for Finitely Generated Nilpotent Minimum Algebras, with Applications

Stefano Aguzzoli

Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39–41, 20135 Milano, Italy. E-mail: aguzzoli{at}dsi.unimi.it

Manuela Busaniche

Instituto de Matemática del Litoral-FIQ, CONICET-UNL, Güemes 3450, S3000GLN, Santa Fe, Argentina. E-mail: manuelabusaniche{at}yahoo.com.ar

Vincenzo Marra

Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39–41, 20135 Milano, Italy. E-mail: marra{at}dico.unimi.it

Received 13 January 2007.


  Abstract

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.

Keywords: Spectral duality; prime spectrum; amalgamation; interpolation; t-norm based logics


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