On Axiomatizing Shramko-Wansing’s Logic
Studia Logica 91 (3):407-428 (2009)
Abstract
This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.DOI
10.1007/s11225-009-9181-6
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Citations of this work
Non-deterministic algebraization of logics by swap structures1.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Logic Journal of the IGPL 28 (5):1021-1059.
The Logic of Generalized Truth Values and the Logic of Bilattices.Sergei P. Odintsov & Heinrich Wansing - 2015 - Studia Logica 103 (1):91-112.
The lattice of Belnapian modal logics: Special extensions and counterparts.Sergei P. Odintsov & Stanislav O. Speranski - 2016 - Logic and Logical Philosophy 25 (1):3-33.
Bi-facial Truth: a Case for Generalized Truth Values.Dmitry Zaitsev & Yaroslav Shramko - 2013 - Studia Logica 101 (6):1299-1318.
Sequent calculi for some trilattice logics.Norihiro Kamide & Heinrich Wansing - 2009 - Review of Symbolic Logic 2 (2):374-395.
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.
How a computer should think.Nuel Belnap - 1977 - In G. Ryle (ed.), Contemporary Aspects of Philosophy. Oriel Press.
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.
