Repairing the interpolation theorem in quantified modal logic

Carlos Areces, Patrick Blackburn, Maarten Marx*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


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 (for example in quantified modal K, T, D, S4, S4.3 and S5 with constant domains), 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.

Original languageEnglish
JournalAnnals of Pure and Applied Logic
Issue number1-3
Pages (from-to)287-299
Number of pages13
Publication statusPublished - 15 Dec 2003
Externally publishedYes


  • Beth definability
  • Bounded fragment
  • Interpolation
  • Quantified hybrid logic
  • Quantified modal logic

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