Bounding Resource Consumption with Gödel-Dummett Logics

Dominique Larchey-Wendling (1)

1 TYPES - Logic, proof Theory and Programming

Gödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted * is explicit and provide an operational semantics which measures the consumption of this resource.We present a linear transformation of a process P into a formula f of LC. We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LCn. Combining this result with our previous results on proof and counter-model construction for LCn, we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LCn.

Domaines: Logique en informatique [cs.LO]; Informatique et langage [cs.CL]; Calcul parallèle, distribué et partagé [cs.DC]

Dominique Larchey-Wendling. Bounding Resource Consumption with Gödel-Dummett Logics. 12th International Conference on Logic for Programming Artificial Intelligence and Reasoning - LPAR'05, Dec 2005, Montego Bay, Jamaica. pp.682-696, ⟨10.1007/11591191_47⟩. ⟨hal-00012536⟩