Metacompleteness of substructural logics
type: Item
instance of: scholarly article
title: Metacompleteness of substructural logics
zbMATH Open document ID: 1268.03024
author: Takahiro Seki
published in: Studia Logica
publication date: 2013-02-18T00:00:00Z
review text: The paper studies the extensions of the logic \(\mathbf{FL}\) -- the logic of full Lambek calculus. A logic \(L\) is said to enjoy the disjunction property if the fact that \(\alpha \lor \beta\) is a theorem of \(L\) entails that \(\alpha\) or \(\beta\) is a theorem of \(L\). A logic \(L\) is said to enjoy the existence property if the fact that \(\exists x\alpha(x)\) is a theorem of \(L\) entails that for some term \(t\), \(\alpha(t)\) is a theorem of \(L\). The metacompleteness of some logics over \(\mathbf{FL}\) is proved. Metacompleteness is used in order to establish disjunction and existence properties (or the absence of these properties) of extensions of \(\mathbf{FL}\). In particular, it is proved that no substructural logic that is both involutive and contractive has the disjunction or the existence property. Also, using metacompleteness, the admissibility of some inference rules is proven.
reviewed by: Alex Citkin
Mathematics Subject Classification ID: 03B47
zbMATH DE Number: 6136992
zbMATH Keywords: metacompleteness
zbMATH Keywords: substructural logics
zbMATH Keywords: disjunction property
zbMATH Keywords: existence property
zbMATH Keywords: admissible rules
MaRDI profile type: Publication
full work available at URL: s11225-012-9458-z
OpenAlex ID: W2094859184
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DOI: 10.1007/S11225-012-9458-Z
description: scientific article; zbMATH DE number 6136992