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There are two known general results on the finite model property (fmp) of commutators $[L_{0},L_{1}]$ (bimodal logics with commuting and confluent modalities). If $L$ is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both $[L,\mathbf{K}]$ and $[L,\mathbf{S5}]$ are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both $L_{0}$ and $L_{1}$ are determined by transitive frames and have frames of arbitrarily large depth, then $[L_{0},L_{1}]$ 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 $[\mathbf{K3},\mathbf{K}]$ 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 $[\mathbf{S4.3},\mathbf{S5}]$ and the decidable product logic $\mathbf{S4.3}\!\times\!\mathbf{S5}$ . We also show cases when already half of commutativity is enough to force infinite frames.

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Project Euclid (Hosted at Cornell University Library)  


Kurucz, Agi - 

Id.: 69790186

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clavemultimodal logic - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2017 University of Notre Dame

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0029-4527
[References] 1939-0726

Fecha de contribución: 16-abr-2017


* Notre Dame J. Formal Logic 58, no. 2 (2017), 287-299
* doi:10.1215/00294527-3870247

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