Bounding Resource Consumption with Gödel-Dummett Logics

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.