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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Research supported by Marie Curie Fellowship Grant HPMF-CT-2004-501043.
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Gabbay, D., Metcalfe, G. Fuzzy logics based on [0,1)-continuous uninorms. Arch. Math. Logic 46, 425–449 (2007). https://doi.org/10.1007/s00153-007-0047-1
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DOI: https://doi.org/10.1007/s00153-007-0047-1