Communication and Concurrency
A Tableau System for Gödel-Dummett Logic Based on a Hypersequent Calculus
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Combining Proof-Search and Counter-Model Construction for Deciding Gödel-Dummett Logic
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Gödel-Dummett Counter-models through Matrix Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
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Gödel-Dummett logic LC and its finite approximations LCnare the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCnlogics 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 LCn. 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.