A few more useful 8-valued logics for reasoning with tetralattice \(EIGHT_{4}\)
type: Item
instance of: scholarly article
title: A few more useful 8-valued logics for reasoning with tetralattice \(EIGHT_{4}\)
zbMATH Open document ID: 1178.03035
author: Dmitry V. Zaitsev
published in: Studia Logica
publication date: 2009-11-16T00:00:00Z
review text: This paper provides a generalization of the initial values of Belnap's \(4\)-valued logic [see \textit{N. D. Belnap}, ``A useful four-valued logic'', in: J. M. Dunn et al. (eds.), Modern uses of multiple-valued logic. Fifth international symposium, Bloomington, 1975, 5--37 (1977; Zbl 0424.03012); ``How a computer should think'', in: G. Ryle (ed.), Contemporary aspects of philosophy. Oriel Press. 30--55 (1977)], based on the idea of Kleene's concept of `logic of uncertainty'. The author arrived at the set of eight generalized truth values which may be regarded even more natural as far as the intuitive perspective is concerned. In order to clarify this generalization, a new algebraic structure, the tetralattice \(EIGHT_4\), is introduced, which combines four different ordering relations defined independently: information ordering, truth ordering, falsity ordering and uncertainty ordering. An adequate axiomatization for this logic is proposed as well.
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03G10
zbMATH DE Number: 5633563
zbMATH Keywords: generalized truth values
zbMATH Keywords: Dunn-Belnap logic
zbMATH Keywords: Shramko-Wansing logic
zbMATH Keywords: bilattice
zbMATH Keywords: trilattice
zbMATH Keywords: tetralattice
zbMATH Keywords: first-degree entailment.
reviewed by: Branislav Boričić
MaRDI profile type: Publication
full work available at URL: s11225-009-9198-x
OpenAlex ID: W2130779558
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DOI: 10.1007/S11225-009-9198-X
description: scientific article; zbMATH DE number 5633563