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FINITE AXIOMATIZABILITY OF TRANSITIVE MODAL LOGICS OF FINITE DEPTH AND WIDTH WITH RESPECT TO PROPER-SUCCESSOR-EQUIVALENCE

Part of: General logic

Published online by Cambridge University Press:  23 June 2023

YAN ZHANG  and
MING XU
YAN ZHANG
Affiliation:
DEPARTMENT OF PHILOSOPHY RENMIN UNIVERSITY OF CHINA BEIJING, P. R. CHINA E-mail: yanzhangsym@gmail.com
MING XU
Affiliation:
DEPARTMENT OF PHILOSOPHY WUHAN UNIVERSITY WUHAN, P. R. CHINA E-mail: mingxu01@hotmail.com
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Abstract

This paper proves the finite axiomatizability of transitive modal logics of finite depth and finite width w.r.t. proper-successor-equivalence. The frame condition of the latter requires, in a rooted transitive frame, a finite upper bound of cardinality for antichains of points with different sets of proper successors. The result generalizes Rybakov’s result of the finite axiomatizability of extensions of $\mathbf {S4}$ of finite depth and finite width.

Keywords

modal logicfinite axiomatizabilitytransitive logics of finite depthtransitive logics of finite suc-eq-width

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 14
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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