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Spring 1998 Failure of Interpolation in Combined Modal Logics
Carlos Areces, Maarten Marx
Notre Dame J. Formal Logic 39(2): 253-273 (Spring 1998). DOI: 10.1305/ndjfl/1039293067


We investigate transfer of interpolation in such combinations of modal logic which lead to interaction of the modalities. Combining logics by taking products often blocks transfer of interpolation. The same holds for combinations by taking unions, a generalization of Humberstone's inaccessibility logic. Viewing first-order logic as a product of modal logics, we derive a strong counterexample for failure of interpolation in the finite variable fragments of first-order logic. We provide a simple condition stated only in terms of frames and bisimulations which implies failure of interpolation. Its use is exemplified in a wide range of cases.


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Carlos Areces. Maarten Marx. "Failure of Interpolation in Combined Modal Logics." Notre Dame J. Formal Logic 39 (2) 253 - 273, Spring 1998.


Published: Spring 1998
First available in Project Euclid: 7 December 2002

zbMATH: 0968.03025
MathSciNet: MR1715019
Digital Object Identifier: 10.1305/ndjfl/1039293067

Primary: 03B45

Rights: Copyright © 1998 University of Notre Dame


Vol.39 • No. 2 • Spring 1998
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