Failure of interpolation in combined modal logics

Marx, M. and Areces, C.. Failure of interpolation in combined modal logics. Notre Dame Journal of Formal Logic, 39(2):253–273, 1998.

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Abstract:

We investigate transfer of interpolation in such combinations of modal logic which lead to interaction of the modalities. Combining logics by taking products often blocks transfer of interpolation. The same holds for combinations by taking unions, a generalization of Humberstone's inaccessibility logic. Viewing first order logic as a product of modal logics, we derive a strong counterexample for failure of interpolation in the finite variable fragments of first order logic. We provide a simple condition stated only in terms of frames and bisimulations which implies failure of interpolation. Its use is exemplified in a wide range of cases.

BibTeX: (download)

@ARTICLE{arec:fail98,
  author = {Marx, M. and Areces, C.},
  title = {Failure of interpolation in combined modal logics},
  journal = {Notre Dame Journal of Formal Logic},
  year = {1998},
  volume = {39},
  pages = {253--273},
  number = {2},
  abstract = {We investigate transfer of interpolation in such combinations of modal
	logic which lead to interaction of the modalities. Combining logics
	by taking products often blocks transfer of interpolation. The same
	holds for combinations by taking unions, a generalization of Humberstone's
	inaccessibility logic. Viewing first order logic as a product of
	modal logics, we derive a strong counterexample for failure of interpolation
	in the finite variable fragments of first order logic. We provide
	a simple condition stated only in terms of frames and bisimulations
	which implies failure of interpolation. Its use is exemplified in
	a wide range of cases.},
}

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