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2017 Bimodal Logics with a “Weakly Connected” Component without the Finite Model Property
Agi Kurucz
Notre Dame J. Formal Logic 58(2): 287-299 (2017). DOI: 10.1215/00294527-3870247


There are two known general results on the finite model property (fmp) of commutators [L0,L1] (bimodal logics with commuting and confluent modalities). If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that commutators with a “weakly connected” component often lack the fmp. Our results imply that the above positive result does not generalize to universally axiomatizable component logics, and even commutators without “transitive” components such as [K3,K] can lack the fmp. We also generalize the above negative result to cases where one of the component logics has frames of depth one only, such as [S4.3,S5] and the decidable product logic S4.3×S5. We also show cases when already half of commutativity is enough to force infinite frames.


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Agi Kurucz. "Bimodal Logics with a “Weakly Connected” Component without the Finite Model Property." Notre Dame J. Formal Logic 58 (2) 287 - 299, 2017.


Received: 9 May 2014; Accepted: 14 October 2014; Published: 2017
First available in Project Euclid: 9 March 2017

zbMATH: 06751304
MathSciNet: MR3634982
Digital Object Identifier: 10.1215/00294527-3870247

Primary: 03B45
Secondary: 03B44, 03B62

Rights: Copyright © 2017 University of Notre Dame


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Vol.58 • No. 2 • 2017
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