Modal tableau calculi and interpolation
type: Item
instance of: scholarly article
title: Modal tableau calculi and interpolation
zbMATH Open document ID: 0547.03015
DOI: 10.1007/BF00249258
author: Wolfgang Rautenberg
published in: Journal of Philosophical Logic
publication date: 1983-01-01T00:00:00Z
review text: The paper shows that all the propositional modal calculi over the language whose connectives are \(\neg\), \(\wedge\), \(\square\) and \(\bigcirc\) (falsum) and which possess a complete tableau system have the interpolation property, provided that the tableau rules satisfy certain conditions. These conditions include a wide class of normal modal calculi. The author also presents tableau systems for several modal calculi (including B, K4, G, Gr and extensions) and proves by constructive methods the completeness of those tableau systems with respect to appropriate Kripke semantics. It is shown, specifically, that the finite model property holds for those systems, which also satisfy the remaining conditions for the interpolation property. The problem of the existence of the interpolation property is discussed for various other examples, in particular for some classes of extensions of K4, G and Gr.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03C40
zbMATH DE Number: 3871325
zbMATH Keywords: propositional modal calculi
zbMATH Keywords: tableau system
zbMATH Keywords: interpolation property
zbMATH Keywords: normal modal calculi
zbMATH Keywords: Kripke semantics
zbMATH Keywords: finite model property
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3871325