Repairing the Interpolation Theorem in Quantified Modal Logic
C. Areces, P. Blackburn, M. Marx
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 (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.
Keywords: quantified modal logic, quantified hybrid logic,
interpolation, Beth definability, bounded fragment