Repairing the interpolation theorem in quantified modal logic

Annals of Pure and Applied Logic 124 (1-3):287-299 (2003)
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Abstract

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

Citations of this work

The Problem of Cross-world Predication.Alexander W. Kocurek - 2016 - Journal of Philosophical Logic 45 (6):697-742.
Natural deduction for first-order hybrid logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
Hybrid Type Theory: A Quartet in Four Movements.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2011 - Principia: An International Journal of Epistemology 15 (2):225.

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References found in this work

Hybrid languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
[Omnibus Review].H. Jerome Keisler - 1970 - Journal of Symbolic Logic 35 (2):342-344.
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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