Natural three-valued logics and classical logic

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N.E. Tomova

Abstract

In this paper implicative fragments of natural three- valued logic are investigated. It is proved that some fragments are equivalent by set of tautologies to implicative fragment of classical logic. It is also shown that some natural three-valued logics verify all tautologies of classical propositional logic.

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References

Devyatkin, L., Three-valued semantics for the classical propositional logic, Moscow: Institute of Philosophy of RAS, 2011 (in Russian).
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Tomova, N., A lattice of implicative extensions of regular Kleene’s logics, Reports on mathematical logic 47:173—182, 2012.
Tomova, N., Implicative extensions of regular Kleene’s logics, Logical Investigations 16:233—258, 2010 (in Russian).
Wajsberg, M., Metalogische Beitr_age, Wiadomo_sci Matematyczne 43: 131–168, 1937. (English translation: Wajsberg, M., Contribution to metalogic, Logical works, Wroc llaw, 1977, pp. 172–200).