Repairing the interpolation theorem in quantified modal logic

Annals of Pure and Applied Logic 124 (1-3):287-299 (2003)
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Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's definability theorem fail in a number of well-known quantified modal logics , their counterparts in quantified hybrid logic have these properties. These are special cases of the main result of the paper: the quantified hybrid logic of any class of frames definable in the bounded fragment of first-order logic has the interpolation property, irrespective of whether varying, constant, expanding, or contracting domains are assumed



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Patrick Blackburn
Roskilde University

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Natural deduction for first-order hybrid logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
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Hybrid languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
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Hierarchies of modal and temporal logics with reference pointers.Valentin Goranko - 1996 - Journal of Logic, Language and Information 5 (1):1-24.
Failures of the interpolation lemma in quantified modal logic.Kit Fine - 1979 - Journal of Symbolic Logic 44 (2):201-206.

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