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

Dov Gabbay, George Metcalfe

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


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.

Original languageEnglish
Pages (from-to)425-449
Number of pages25
JournalArchive for Mathematical Logic
Issue number5-6
StatePublished - Jul 2007
Externally publishedYes


  • Cross ratio
  • Fuzzy logic
  • Uninorm
  • t-Norm


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