Repairing the interpolation theorem in quantified modal logic Original Research Article

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 Bethʹs 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.