Repairing the interpolation Theorem in Quantified Modal Logic

C. Areces, P. Blackburn, and M. Marx. Repairing the interpolation Theorem in Quantified Modal Logic. Annals of Pure and Applied Logics, 123(1--3):287–299, 2003.

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Abstract

Quantified hybrid logic is quantified modal logic extended with apparatus for nam- ing 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 interpo- lation property, irrespective of whether varying, constant, expanding, or contracting domains are assumed.

BibTeX

@Article{Areces2003b,
  author =       "C. Areces and P. Blackburn and M. Marx",
  journal =      "Annals of Pure and Applied Logics",
  title =        "Repairing the interpolation Theorem in Quantified
                 Modal Logic",
  year =         "2003",
  abstract =     "Quantified hybrid logic is quantified modal logic
                 extended with apparatus for nam- ing 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 interpo- lation property, irrespective of
                 whether varying, constant, expanding, or contracting
                 domains are assumed.",
  number =       "1--3",
  pages =        "287--299",
  volume =       "123",
}