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Natural Deduction and Normalisation for Partially Commutative Linear Logic and Lambek Calculus with Product

hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierLinguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
dc.contributor.authorAMBLARD, Maxime
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierLinguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
dc.contributor.authorRETORÉ, Christian
dc.contributor.editorS. B. Cooper and T. F. Kent and B. Löwe and A. Sorbi
dc.date.accessioned2024-04-15T09:50:45Z
dc.date.available2024-04-15T09:50:45Z
dc.date.created2007-06-11
dc.date.issued2007-06-18
dc.date.conference2007-06-18
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/198370
dc.description.abstractEnThis paper provides a natural deduction system for Partially Commutative Intuitionistic Multiplicative Linear Logic (PCIMLL) and establishes its normalisation and subformula property. Such a system in- volves both commutative and non commutative connectives and deals with context that are series-parallel multisets of formulæ. This calcu- lus is the extension of the one introduced by de Groote presented by the second order for modelling Petri net execution, with a full entropy which allow order to be relaxed into any suborder — as opposed to the Non Commutative Logic of Abrusci and Ruet. Our result also includes, as a special case, the normalisation of natural deduction the Lambek calculus with product, which is unsurprising but yet unproved. Up to now PCIMLL with full entropy had no natural deduction. In particular for linguistic applications, such a syntax is much welcome to construct semantic representations from syntactic analyses.
dc.language.isoen
dc.publisherUniversità di Siena
dc.source.titleComputation and Logic in the Real World (Computing in Europe 2007)
dc.subject.enlogi
dc.subject.enproof theory
dc.subject.enlinear logic
dc.subject.enLambek calculus
dc.title.enNatural Deduction and Normalisation for Partially Commutative Linear Logic and Lambek Calculus with Product
dc.typeCommunication dans un congrès
dc.subject.halInformatique [cs]/Logique en informatique [cs.LO]
dc.subject.halMathématiques [math]/Logique [math.LO]
bordeaux.page28--44
bordeaux.hal.laboratoriesLaboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800*
bordeaux.issueID487
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleComputation and Logic in the Real World (Computing in Europe 2007)
bordeaux.countryIT
bordeaux.title.proceedingComputation and Logic in the Real World (Computing in Europe 2007)
bordeaux.conference.citySiena
bordeaux.peerReviewedoui
hal.identifierhal-00409486
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2007-06-23
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00409486v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Computation%20and%20Logic%20in%20the%20Real%20World%20(Computing%20in%20Europe%202007)&rft.date=2007-06-18&rft.issue=ID487&rft.spage=28--44&rft.epage=28--44&rft.au=AMBLARD,%20Maxime&RETOR%C3%89,%20Christian&rft.genre=unknown


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