The Logic of Generalized Truth Values and the Logic of Bilattices
Studia Logica 103 (1):91-112 (2015)
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, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive bilattices with conflationAuthor's Profile
DOI
10.1007/s11225-014-9546-3
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Citations of this work
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The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2019 - Journal of Philosophical Logic 48 (5):787-808.
Conservative translations of four-valued logics in modal logic.Ekaterina Kubyshkina - 2019 - Synthese 198 (S22):5555-5571.
References found in this work
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
Some Useful 16-Valued Logics: How a Computer Network Should Think.Yaroslav Shramko & Heinrich Wansing - 2005 - Journal of Philosophical Logic 34 (2):121-153.
Notes on N-lattices and constructive logic with strong negation.D. Vakarelov - 1977 - Studia Logica 36 (1-2):109-125.
Hyper-contradictions, generalized truth values and logics of truth and falsehood.Yaroslav Shramko & Heinrich Wansing - 2006 - Journal of Logic, Language and Information 15 (4):403-424.
