Fuzzy logics based on [0,1)-continuous uninorms

Archive for Mathematical Logic 46 (5-6):425-449 (2007)

Abstract

Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1), generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics.

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Author's Profile

Dov Gabbay
Hebrew University of Jerusalem

References found in this work

Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
A Constructive Analysis of RM.Arnon Avron - 1987 - Journal of Symbolic Logic 52 (4):939 - 951.
Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.
Analytic Calculi for Product Logics.George Metcalfe, Nicola Olivetti & Dov Gabbay - 2004 - Archive for Mathematical Logic 43 (7):859-889.
Complexity of T-Tautologies.Matthias Baaz, Petr Hájek, Franco Montagna & Helmut Veith - 2001 - Annals of Pure and Applied Logic 113 (1-3):3-11.

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Citations of this work

Mathematical Fuzzy Logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.
Generalized Ordinal Sums and Translations.Nikolaos Galatos - 2011 - Logic Journal of the IGPL 19 (3):455-466.

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