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Finite frames for K4.3 × S5 are decidable

Research output: Chapter in Book/Report/Conference proceedingConference paper

Agi Kurucz, Sérgio Marcelino

Original languageEnglish
Title of host publicationAdvances in Modal Logic
EditorsTorben Brauner, Lawrence Moss, Thomas Bolander, Silvio Ghilardi
PublisherCollege Publications
Pages411-436
Number of pages26
ISBN (Electronic)9781848900684
Publication statusPublished - 1 Jan 2014
Event9th Conference on Advances in Modal Logic, AiML 2012 - Copenhagen, Denmark
Duration: 22 Aug 201225 Aug 2012

Publication series

NameAdvances in Modal Logic
Volume9

Conference

Conference9th Conference on Advances in Modal Logic, AiML 2012
CountryDenmark
CityCopenhagen
Period22/08/201225/08/2012

King's Authors

Abstract

If a modal logic L is finitely axiomatisable, then it is of course decidable whether a finite frame is a frame for L: one just has to check the finitely many axioms in it. If L is not finitely axiomatisable, then this might not be the case. For example, it is shown in [7] that the finite frame problem is undecidable for every L between the product logics K × K × K and S5 × S5 × S5. Here we show that the finite frame problem for the modal product logic K4.3 × S5 is decidable. K4.3 × S5 is outside the scope of both the finite axiomatisation results of [4], and the non-finite axiomatisability results of [11]. So it is not known whether K4.3 × S5 is finitely axiomatisable. Here we also discuss whether our results bring us any closer to either proving non-finite axiomatisability of K4.3×S5, or finding an explicit, possibly infinite, axiomatisation of it.

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