Studia Logica

, Volume 103, Issue 1, pp 91–112 | Cite as

The Logic of Generalized Truth Values and the Logic of Bilattices

  • Sergei P. OdintsovEmail author
  • Heinrich Wansing


This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \({\models_t}\) and \({\models_f}\) , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, J Philos Logic, 34:121–153, 2005). The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive bilattices with conflation (Rivieccio, 2010).


Bilattices Trilattices Generalized truth values Twist-structures Axiomatization 


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Department of Philosophy IIRuhr UniversityBochumGermany

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