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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:

Hybrid logics are extensions of orthodox modal logics in which it is possible to name and bind worlds. We investigate hybridization of first-order modal logics and show that as far as interpolation is concerned, hybridization improves the behavior of the underlying modal logic, allowing us to repair failures of interpolation in a very general way. As a corollary of a general interpolation theorem for first-order hybrid logics, we prove that hybridization help us repair all counterexamples to interpolation discussed by Fine in [1]. In particular, first-order hybrid K, T, S4 and S5 all enjoy interpolation, no matter what domain condition we impose. [1] Fine, K.. Failures of the interpolation lemma in quantified modal logic. Journal of Symbolic Logic, 44(2):201--206, 1979.

BibTeX: (download)

@ARTICLE{areces03:_repair_theor_quant_modal_logic,
  author = {C. Areces and P. Blackburn and M. Marx},
  title = {Repairing the interpolation Theorem in Quantified Modal Logic},
  journal = {Annals of Pure and Applied Logics},
  year = {2003},
  volume = {123},
  pages = {287--299},
  number = {1--3},
  abstract = {
	Hybrid logics are extensions of orthodox modal logics in which it
	is possible to name and bind worlds. We investigate hybridization
	of first-order modal logics and show that as far as interpolation
	is concerned, hybridization improves the behavior of the underlying
	modal logic, allowing us to repair failures of interpolation in a
	very general way.
	As a corollary of a general interpolation theorem for first-order
	hybrid logics, we prove that hybridization help us repair all counterexamples
	to interpolation discussed by Fine in [1]. In particular, first-order
	hybrid K, T, S4 and S5 all enjoy interpolation, no matter what domain
	condition we impose.
	[1] Fine, K.. Failures of the interpolation lemma in quantified modal
	logic. Journal of Symbolic Logic, 44(2):201--206, 1979. }
}

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