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, $${\models_t}$$ ? t and $${\models_f}$$ ? 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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