PP-1999-04: Labelled Tableau Calculi Generating Simple Models for Substructural Logics

PP-1999-04: Terui, Kazushige (1999) Labelled Tableau Calculi Generating Simple Models for Substructural Logics. [Report]

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In this paper we apply the methodology of Labelled Deductive Systems to the
tableau method in order to obtain a deductive framework for substructural
logics which incorporates the facility of model generation. For this
special purpose, we propose new labelled tableau calculi TL and TLe for two
substructural logics L (essentially the Lambek calculus) and Le (the
multiplicative fragment of intuitionistic linear logic). The use of labels
makes it possible to generate countermodels in terms of a certain very
simple semantics based on monoids, which we call the simple semantics. We
show that, given a formula C as input, every nonredundant tableau
construction procedure for TL and TLe terminates in finitely many steps,
yielding either a tableau proof of C or a finite countermodel of C in
terms of the simple semantics. It shows the finite model property for L
and Le with respect to the simple semantics.

Item Type: Report
Report Nr: PP-1999-04
Series Name: Prepublication (PP) Series
Year: 1999
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/4

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