Constructive Interpolation in Hybrid Logic
Patrick Blackburn, Maarten Marx
Abstract:
Craig's interpolation lemma fails for many propositional and first order
modal logics. The interpolation property is often regarded as a sign of
well-matched syntax and semantics. Hybrid logicians claim that modal logic
is missing important syntactic machinery, namely tools for referring to
worlds, and that adding such machinery solves many technical problems. The
paper presents strong evidence for this claim by defining interpolation
algorithms for both propositional and first order hybrid logic. These
algorithms produce interpolants for the hybrid logic of every elementary
class of frames satisfying the property that a frame is in the class if
and only if all its point-generated subframes are in the class. In addition,
on the class of all frames, the basic algorithm is conservative: on purely
modal input it computes interpolants in which the hybrid syntactic
machinery does not occur.