Patrick Blackburn

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, 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.

In this paper we argue that Prior and Reichenbach are best viewed as allies, not antagonists. We do so by combining the central insights of Prior and Reichenbach in the framework of hybrid tense logic. This overcomes a well-known defect of Reichenbach’s tense schema, namely that it gives multiple representations to sentences in the future perfect and the future-in-the-past. It also makes it easy to define an iterative schema for tense that allows for multiple points of reference, a possibility noted by Prior and demanded by Comrie, and we sketch how this schema can be generalized to a shift-and-restrict pattern in which special propositional symbols act as restrictors on the range of tense operators.