First-order da Costa logic
type: Item
instance of: scholarly article
title: First-order da Costa logic
zbMATH Open document ID: 1218.03024
author: Graham Priest
published in: Studia Logica
publication date: 2011-03-14T00:00:00Z
review text: In an earlier paper, Priest altered the clause \(v_w(\lnot\alpha) = 1\) iff for all \(w'\) such that \(wRw'\), \(v_{w'}(\alpha) = 0\), of the Kripke semantics for intuitionistic propositional logic, to \(v_w(\lnot\alpha) = 1\) iff for some \(w'\) such that \(w'Rw\), \(v_{w'}(\alpha) = 0\). (Here \(v_w\) is an evaluation that, at a world \(w\), maps formulas into \(\{0,1\}\).) The result is the semantics of a paraconsistent propositional logic he calls da Costa logic, which is an extension of da Costa's logic \(C_{\omega}\). In this paper, the author extends this semantics to one for a first-order predicate logic, which he also presents as a tableau and a natural deduction system. He proves that the semantics is sound and complete. While the \(\to\)-free fragment of propositional da Costa logic is the same as that of classical propositional logic, the paper produces the surprising result that not even the logical truths of the \(\forall\)-\(\lor\)-\(\land\)-\(\lnot\) or \(\exists\)-\(\lor\)-\(\land\)-\(\lnot\) fragments of predicate da Costa logic are identical to those of classical predicate logic.
reviewed by: Martin W. Bunder
Mathematics Subject Classification ID: 03B53
zbMATH DE Number: 5865396
zbMATH Keywords: da Costa logic
zbMATH Keywords: paraconsistent logic
zbMATH Keywords: semantics
MaRDI profile type: Publication
full work available at URL: s11225-010-9303-1
OpenAlex ID: W2075998444
cites work: Anti-intuitionism and paraconsistency
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cites work: Q3518425
cites work: Applications of Kripke models to Heyting-Brouwer logic
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cites work: Dual-intuitionistic logic
DOI: 10.1007/S11225-010-9303-1
description: scientific article; zbMATH DE number 5865396