Aspects of analytic deduction
type: Item
instance of: scholarly article
title: Aspects of analytic deduction
zbMATH Open document ID: 0872.03036
DOI: 10.1007/BF00265254
author: Athanassios Tzouvaras
published in: Journal of Philosophical Logic
publication date: 1997-02-20T00:00:00Z
review text: For any set of formulae \(\Gamma\cup\{A\}\), the deduction \(\Gamma\lvdash A\) is called analytic, if, roughly, every atomic subformula of \(A\) is already contained in the set of subformulae of \(\Gamma\). In this paper, the author gives a formal description of an analytic subrelation of the classical first-order logic consequence relation. This formalization is presented as a subsystem of Gentzen's sequent calculus \({\mathbf L}{\mathbf K}\) for classical logic by the corresponding restrictions on non-analytic rules of \({\mathbf L}{\mathbf K}\). The main result of the paper, regarding the correct axiomatization of the analytic classical consequence relation, can be considered as a new fine example of Gentzen's cut-elimination theorem application. The relationship between the semantic and syntactic aspects of the analytic deduction relation is discussed as well.
reviewed by: Branislav Boričić
Mathematics Subject Classification ID: 03F05
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03B60
zbMATH DE Number: 980787
zbMATH Keywords: subsystem of Gentzen's sequent calculus \({\mathbf L}{\mathbf K}\)
zbMATH Keywords: restrictions on non-analytic rules
zbMATH Keywords: cut-elimination
zbMATH Keywords: analytic deduction
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 980787