Failure of Interpolation in Combined Modal Logics

Notre Dame Journal of Formal Logic 39 (2):253-273 (1998)
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Abstract

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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References found in this work

Products of modal logics, part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
Modal definability in enriched languages.Valentin Goranko - 1989 - Notre Dame Journal of Formal Logic 31 (1):81-105.

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