Constructive Interpolation in Hybrid Logic

Constructive Interpolation in Hybrid Logic (2002)

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by Patrick Blackburn , Maarten Marx

Venue:	Journal of Symbolic Logic
Citations:	7 - 2 self

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@ARTICLE{Blackburn02constructiveinterpolation,
    author = {Patrick Blackburn and Maarten Marx},
    title = {Constructive Interpolation in Hybrid Logic},
    journal = {Journal of Symbolic Logic},
    year = {2002},
    volume = {68},
    pages = {2003}
}

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Abstract

Craig's interpolation lemma (if φ → ψ is valid, then φ → θ and θ → ψ are valid, for θ a formula constructed using only primitive symbols which occur both in φ and ψ) 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.

Keyphrases

hybrid logic constructive interpolation well-matched syntax elementary class first order hybrid logic hybrid logician basic algorithm hybrid syntactic machinery many technical problem primitive symbol interpolation algorithm strong evidence interpolation lemma algorithm produce interpolants modal input important syntactic machinery interpolation property first order modal logic modal logic point-generated subframes