Review of Symbolic Logic 2 (2):374-395 (2009)

Authors
Heinrich Wansing
Ruhr-Universität Bochum
Abstract
The trilattice SIXTEEN3 introduced in Shramko & Wansing (2005) is a natural generalization of the famous bilattice FOUR2. Some Hilbert-style proof systems for trilattice logics related to SIXTEEN3 have recently been studied (Odintsov, 2009; Shramko & Wansing, 2005). In this paper, three sequent calculi GB, FB, and QB are presented for Odintsovs coordinate valuations associated with valuations in SIXTEEN3. The equivalence between GB, FB, and QB, the cut-elimination theorems for these calculi, and the decidability of B are proved. In addition, it is shown how the sequent systems for B can be extended to cut-free sequent calculi for Odintsov’s LB, which is an extension of B by adding classical implication and negation connectives.
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DOI 10.1017/S1755020309090212
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References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.

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Citations of this work BETA

Analytic Tableaux for All of SIXTEEN 3.Stefan Wintein & Reinhard Muskens - 2015 - Journal of Philosophical Logic 44 (5):473-487.
The Power of Belnap: Sequent Systems for SIXTEEN ₃. [REVIEW]Heinrich Wansing - 2010 - Journal of Philosophical Logic 39 (4):369 - 393.
Generalized Truth Values.: A Reply to Dubois.Heinrich Wansing & Nuel Belnap - 2010 - Logic Journal of the IGPL 18 (6):921-935.
Gentzenization of Trilattice Logics.Mitio Takano - 2016 - Studia Logica 104 (5):917-929.

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