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The Logic of Generalized Truth Values and the Logic of Bilattices

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Abstract

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).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyug prosp. 4, 630090, Novosibirsk, Russia

    Sergei P. Odintsov

  2. Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia

    Sergei P. Odintsov

  3. Department of Philosophy II, Ruhr University, Bochum Universitätsstraße 150, 44780, Bochum, Germany

    Heinrich Wansing

Authors
  1. Sergei P. Odintsov
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  2. Heinrich Wansing
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Correspondence to Sergei P. Odintsov.

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Odintsov, S.P., Wansing, H. The Logic of Generalized Truth Values and the Logic of Bilattices. Stud Logica 103, 91–112 (2015). https://doi.org/10.1007/s11225-014-9546-3

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