Connection Methods in Linear Logic and Proof nets Construction

Didier Galmiche 1
1 TYPES - Logic, proof Theory and Programming
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Linear logic (LL) is the logical foundation of some type-theoretic languages and also of environments for specification and theorem proving. In this paper, we analyse the relationships between the proof net notion of LL and the connection notion used for efficient proof-search in different logics. Aiming at using proof nets as a tool for automated deduction in linear logic, we define a connection-based characterization of provability in Multiplicative Linear Logic (MLL). We show that an algorithm for proof net construction can be seen as a proof-search connection method. This central result is illustrated with a specific algorithm that is able to construct, for a provable MLL sequent,a set of connections, a proof net and a sequent proof. From these results we expect to extend to other LL fragments, we analyse what happens with the additive connectives of LL by tackling the additive fragment in a similar way.
Type de document :
Article dans une revue
Theoretical Computer Science, Elsevier, 2000, 232 (1-2), pp.231-272
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https://hal.inria.fr/inria-00099205
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:51:43
Dernière modification le : jeudi 17 mai 2018 - 12:52:03

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  • HAL Id : inria-00099205, version 1

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Didier Galmiche. Connection Methods in Linear Logic and Proof nets Construction. Theoretical Computer Science, Elsevier, 2000, 232 (1-2), pp.231-272. 〈inria-00099205〉

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