InforLorV4, Main, Exploration, bibRecord, 004739

Normalization and sub-formula property for Lambek with product and PCMLL -- Partially Commutative Multiplicative Linear Logic

Identifieur interne : 004739 ( Main/Exploration ); précédent : 004738; suivant : 004740

Normalization and sub-formula property for Lambek with product and PCMLL -- Partially Commutative Multiplicative Linear Logic

Auteurs : Maxime Amblard [France] ; Christian Retoré [France]

Source :

RBID : Hal:hal-00941206

Abstract

This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de Groote and as opposed to the classical version by Abrusci and Ruet admits a full entropy which allow order to be relaxed into any suborder. Our result also includes, as a special case, the normalisation of natural deduction the Lambek calculus with product, which is unsurprising but yet unproved. Regarding Intuitionistic Non Commutative Logic with full entropy does not have up to now a proof net syntax, and that for linguistic applications, sequent calculi which are only more or less equivalent to natural deduction, are not convenient because they lack the standard Curry-Howard isomorphism.

Url:

https://hal.archives-ouvertes.fr/hal-00941206

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 003617
to stream Hal, to step Curation: 003617
to stream Hal, to step Checkpoint: 003860
to stream Main, to step Merge: 004887
to stream Main, to step Curation: 004739

Le document en format XML

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   |texte=   Normalization and sub-formula property for Lambek with product and PCMLL -- Partially Commutative Multiplicative Linear Logic
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Normalization and sub-formula property for Lambek with product and PCMLL -- Partially Commutative Multiplicative Linear Logic

Normalization and sub-formula property for Lambek with product and PCMLL -- Partially Commutative Multiplicative Linear Logic

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Abstract

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Le document en format XML

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