Provability and Countermodels in Gödel-Dummett Logics

Didier Galmiche (1) , Dominique Larchey-Wendling (1) , Yakoub Salhi (1)

1 TYPES - Logic, proof Theory and Programming

Hypersequent calculi, that are a generalization of sequent calculi, have been studied for Gödel-Dummett logics LC and LCn. In this paper we propose a new characterization of validity in these logics from the construction of particular bi-colored graphs associated to hypersequents and the search of specific chains in such graphs. It leads to other contributions that are a new hypersequent calculus and a related tableau system for LCn.We mainly study the class of so-called basic hypersequents and then we generalize our approach to hypersequents.

Domaines: Logique en informatique [cs.LO]

Didier Galmiche, Dominique Larchey-Wendling, Yakoub Salhi. Provability and Countermodels in Gödel-Dummett Logics. International Workshop on Disproving: Non-theorems, Non-validity, Non-Provability - DISPROVING'07, Jul 2007, Bremen, Germany. pp.35-52. ⟨hal-00580307⟩