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LYNDON INTERPOLATION PROPERTY FOR EXTENSIONS OF
$\mathbf {S4}$ AND INTERMEDIATE PROPOSITIONAL LOGICS
- Part of
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- Journal:
- The Journal of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 12 August 2025, pp. 1-33
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- Article
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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.
