Provability and Countermodels in Gödel-Dummett Logics
Identifieur interne : 006B74 ( Hal/Curation ); précédent : 006B73; suivant : 006B75Provability and Countermodels in Gödel-Dummett Logics
Auteurs : Didier Galmiche [France] ; Dominique Larchey-Wendling [France] ; Yakoub Salhi [France]Source :
Abstract
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.
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<front><div type="abstract" xml:lang="en">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.</div>
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