The power of Belnap: sequent systems for \(SIXTEEN_{3 }\)
type: Item
instance of: scholarly article
title: The power of Belnap: sequent systems for \(SIXTEEN_{3 }\)
zbMATH Open document ID: 1200.03019
published in: Journal of Philosophical Logic
publication date: 2010-10-06T00:00:00Z
review text: The trilattice \(SIXTEEN_3\) is a natural generalization of Belnap and Dunn's four-valued logic, called useful four-valued logic (see [\textit{N. D. Belnap}, ``A useful four-valued logic'', in: J. M. Dunn et al. (eds.), Mod. uses of multiple-valued logic, 5th int. symp., Bloomington 1975, 5--37 (1977; Zbl 0424.03012)], [\textit{J. M. Dunn}, ``Intuitive semantics for first-degree entailment and `coupled trees'{}'', Philosophical Studies 29, 149--168 (1976)]), based on the bilattice \(FOUR_2\) (see [\textit{M. Ginsberg}, ``Multivalued logics: a uniform appoach to reasoning in AI'', Computer Intelligence 4, 256--316 (1988)], [\textit{O. Arieli} and \textit{A. Avron}, ``Reasoning with logical bilattices'', J. Logic Lang. Inf. 5, No.~1, 25--63 (1996; Zbl 0851.03017)]). The author presents sound and complete cut-free sequent calculi for truth entailment and falsity entailment in \(SIXTEEN_3\).
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03G10
zbMATH DE Number: 5796519
zbMATH Keywords: cut-free sequent calculus
zbMATH Keywords: soundness
zbMATH Keywords: completeness
zbMATH Keywords: Belnap and Dunn's four-valued logic
zbMATH Keywords: bilattice \(FOUR_2\)
zbMATH Keywords: trilattice \(SIXTEEN_3\)
zbMATH Keywords: generalized truth values
zbMATH Keywords: truth entailment
zbMATH Keywords: falsity entailment
zbMATH Keywords: twist-structure
author: Heinrich Wansing
reviewed by: Branislav Boričić
MaRDI profile type: Publication
full work available at URL: s10992-010-9139-1
OpenAlex ID: W2002719201
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DOI: 10.1007/S10992-010-9139-1
description: scientific article; zbMATH DE number 5796519