Proof nets without links for Lambek calculus and partially commutative linear logic

Daniele Porello (1, 2) , Christian Retoré (1, 2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 SIGNES - Linguistic signs, grammar and meaning: computational logic for natural language

Proof nets wothout links turn algebraic properties of the connectives like assocativity into proof equality. We recall similar results for multiplicative linear logic and for Lambek syntactic calculus before providing an almost complete solution for partially commutative linear logic which contains both commutative and non commutative connectives.

Mots clés: Lambek syntactic calculus; categorial grammar; linear logic

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]

Daniele Porello, Christian Retoré. Proof nets without links for Lambek calculus and partially commutative linear logic. 50 years of the Syntactic calculus, Jul 2008, Chieti, Italy. ⟨hal-00409487⟩