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Games for Inclusion Logic and Fixed-Point Logic

In: Dependence Logic

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  • Erich Grädel

    (RWTH Aachen University, Math. Foundations of Computer Science)

Abstract

One of the most intriguing results on logics of dependence and independence is the tight connection between inclusion logic and the least fixed-point logic LFP. Here we re-examine this connection from a game-theoretic point of view. We study the model-checking games for inclusion logic and for posGFP, the fragment of LFP that uses only (non-negated) greatest fixed points. We show that the evaluation problems for both logics can be represented by a special kind of trap condition in safety games. We then study interpretation arguments for games. In combination with our study of traps for inclusion logic and posGFP, game interpretations will give us a model-theoretic construction of translations between the two logics.

Suggested Citation

  • Erich Grädel, 2016. "Games for Inclusion Logic and Fixed-Point Logic," Springer Books, in: Samson Abramsky & Juha Kontinen & Jouko Väänänen & Heribert Vollmer (ed.), Dependence Logic, pages 73-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31803-5_5
    DOI: 10.1007/978-3-319-31803-5_5
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