Fuzzy logics based on [0,1)-continuous uninorms |
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Authors: | Dov Gabbay George Metcalfe |
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Affiliation: | (1) Department of Computer Science, King’s College London, Strand, London, WC2R 2LS, UK;(2) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA |
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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. Research supported by Marie Curie Fellowship Grant HPMF-CT-2004-501043. |
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Keywords: | Uninorm t-Norm Fuzzy logic Cross ratio |
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