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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 3, Pages 134–159 (Mi izv8476)  

Partitioning Kripke frames of finite height

A. V. Kudinovabc, I. B. Shapirovskya

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics" (HSE), Moscow
c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: In this paper we prove the finite model property and decidability of a family of modal logics. A binary relation $R$ is said to be pretransitive if $R^*=\bigcup_{i\leqslant m} R^i$ for some $m\geqslant 0$, where $R^*$ is the transitive reflexive closure of $R$. By the height of a frame $(W,R)$ we mean the height of the preorder $(W,R^*)$. We construct special partitions (filtrations) of pretransitive frames of finite height, which implies the finite model property and decidability of their modal logics.

Keywords: modal logic, finite model property, decidability, pretransitive relation, finite height.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
This research was carried out in the IITP RAS at the expense of a grant of the Russian Science Foundation (project no. 14-50-00150).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8476

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English version:
Izvestiya: Mathematics, 2017, 81:3, 592–617

Bibliographic databases:

UDC: 510.643
MSC: 03B45
Received: 19.11.2015

Citation: A. V. Kudinov, I. B. Shapirovsky, “Partitioning Kripke frames of finite height”, Izv. RAN. Ser. Mat., 81:3 (2017), 134–159; Izv. Math., 81:3 (2017), 592–617

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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