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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
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


Conference9th Conference on Advances in Modal Logic, AiML 2012

King's Authors


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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