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LYNDON INTERPOLATION PROPERTY FOR EXTENSIONS OF $\mathbf {S4}$ AND INTERMEDIATE PROPOSITIONAL LOGICS

Part of: Model theory General logic

Published online by Cambridge University Press:  12 August 2025

TAISHI KURAHASHI
TAISHI KURAHASHI*
Affiliation:
GRADUATE SCHOOL OF SYSTEM INFORMATICS KOBE UNIVERSITY 1-1 ROKKODAI, NADA, KOBE 657-8501, JAPAN
*
E-mail: kurahashi@people.kobe-u.ac.jp
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Abstract

We study the Lyndon interpolation property (LIP) and the uniform LIP (ULIP) for extensions of $\mathbf {S4}$ and intermediate propositional logics. We prove that among the 18 consistent normal modal logics of finite height extending $\mathbf {S4}$ known to have CIP, 11 logics have LIP and 7 logics do not. We also prove that for intermediate propositional logics, the Craig interpolation property, LIP, and ULIP are equivalent.

Keywords

interpolation propertiesmodal logicintermediate logics

MSC classification

Primary: 03B45: Modal logic (including the logic of norms) 03B55: Intermediate logics 03C40: Interpolation, preservation, definability

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Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 33
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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