Natural Deduction and Normalisation for Partially Commutative Linear Logic and Lambek Calculus with Product
AMBLARD, Maxime
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
RETORÉ, Christian
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
AMBLARD, Maxime
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
RETORÉ, Christian
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
< Réduire
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Langue
en
Communication dans un congrès
Ce document a été publié dans
Computation and Logic in the Real World (Computing in Europe 2007), Computation and Logic in the Real World (Computing in Europe 2007), Computation and Logic in the Real World (Computing in Europe 2007), 2007-06-18, Siena. 2007-06-18 n° ID487, p. 28--44
Università di Siena
Résumé en anglais
This 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 ...Lire la suite >
This 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.< Réduire
Mots clés en anglais
logi
proof theory
linear logic
Lambek calculus
Origine
Importé de halUnités de recherche