David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 18 (4):465-491 (2009)
We consider the model checking problem for Hybrid Logic. Known algorithms so far are global in the sense that they compute, inductively, in every step the set of all worlds of a Kripke structure that satisfy a subformula of the input. Hence, they always exploit the entire structure. Local model checking tries to avoid this by only traversing necessary parts of the input in order to establish or refute the satisfaction relation between a given world and a formula. We present a framework for local model checking of Hybrid Logic based on games. We show that these games are simple reachability games for ordinary Hybrid Logic and weak Büchi games for Hybrid Logic with operators interpreted over the transitive closure of the accessibility relation of the underlying Kripke frame, and show how to solve these games thus solving the local model checking problem. Since the first-order part of Hybrid Logic is inherently hard to localise in model checking, we give examples, in the end, of how global model checkers can be optimised in certain special cases using well-established techniques like fixpoint approximations and divide-and-conquer algorithms.
|Keywords||Local model checking Büchi games|
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References found in this work BETA
Nicole Bidoit, Serenella Cerrito & Virginie Thion (2004). A First Step Towardsmodeling Semistructured Data in Hybrid Multimodal Logic. Journal of Applied Non-Classical Logics 14 (4):447-475.
R. A. Bull (1970). An Approach to Tense Logic. Theoria 36 (3):282-300.
Valentin Goranko (1996). Hierarchies of Modal and Temporal Logics with Reference Pointers. Journal of Logic, Language and Information 5 (1):1-24.
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