Graph-based decision for Gödel-Dummett logics

Dominique Larchey-Wendling (1)

1 TYPES - Logic, proof Theory and Programming

We present a graph-based decision procedure for Gödel-Dummett logics and an algorithm to compute counter-models. A formula is transformed into a conditional bi-colored graph in which we detect some specific cycles and alternating chains using matrix computations. From an instance graph containing no such cycle (resp. no (n+1)-alternating chain) we extract a counter-model in LC (resp. LCn).

Mots clés: Gödel-Dummett logic; sequent calculus; decision procedures; graphs; countermodels

Domaines: Logique en informatique [cs.LO]; Intelligence artificielle [cs.AI]

Dominique Larchey-Wendling. Graph-based decision for Gödel-Dummett logics. Journal of Automated Reasoning, 2007, 38 (1-3), pp.201-225. ⟨10.1007/s10817-006-9047-9⟩. ⟨hal-00105564⟩