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

Published online by Cambridge University Press:  12 August 2025

TAISHI KURAHASHI*
Affiliation:
GRADUATE SCHOOL OF SYSTEM INFORMATICS https://ror.org/03tgsfw79 KOBE UNIVERSITY 1-1 ROKKODAI, NADA, KOBE 657-8501, JAPAN

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.

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© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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