Archive for Mathematical Logic

, Volume 46, Issue 5–6, pp 425–449

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



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.


Uninorm t-Norm Fuzzy logic Cross ratio 

Mathematics Subject Classification (2000)

03B50 03B47 03B52 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceKing’s College LondonLondonUK
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA

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