Refutation systems in modal logic
type: Item
instance of: scholarly article
title: Refutation systems in modal logic
zbMATH Open document ID: 0803.03005
DOI: 10.1007/BF01054714
published in: Studia Logica
publication date: 1995-01-03T00:00:00Z
review text: Refutation systems are deductive systems which infer refutable statements instead of valid statements. Thus, a refutation system is every pair consisting of a set of axioms \(\ldashv\varphi\) and a set of refutation rules: If \(\lvdash\varphi_ 1,\dots,\lvdash \varphi_ k\), \(\ldashv \psi_ 1,\dots,\ldashv \psi_ n\), then \(\ldashv\psi\). The paper contains a historical part on refutation logics and general considerations about such deductive systems. Refutation systems are proposed for various logics. The second part of the paper deals with Gentzen-style refutation rules being a new approach in the area. Besides the cited references, the following technical report may be useful: \textit{Tomasz Skura}: ``Refutation procedures for intuitionistic and modal logics'' [Konstanzer Berichte Logik und Information 37, Universität Konstanz, Zentrum Philosophie und Wissenschaftstheorie].
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 590924
zbMATH Keywords: characterization
zbMATH Keywords: completeness
zbMATH Keywords: deductive systems
zbMATH Keywords: refutation logics
zbMATH Keywords: Gentzen-style refutation rules
author: Valentin Goranko
reviewed by: Uwe Scheffler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 590924