POGODALLA, Sylvain; RETORÉ, Christian

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POGODALLA, Sylvain
Linear logic, proof networks and categorial grammars [CALLIGRAMME]

RETORÉ, Christian
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]

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2004p. 25

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This paper provides a definition of proof-nets for non-commutative linear logic (cyclic linear logic and Lambek calculus) where there are no links, that are small graphs representing the connectives. Instead of a tree like representation with links, the formula is depicted as a graph representing the conclusion up to the algebraic properties of the connectives. In the commutative case the formula is viewed as a cograph. In the non-commutative case it is a more complicated kind of graph which is, roughly speaking, a directed cograph. The criterion consists in the commutative condition plus a bracketing condition.< Leer menos

Palabras clave en inglés

proof theory

linear logic

graph theory

perfect matching

cographs

cyclic orders

computational linguistics

lambek calculus

categorial grammars

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Handsome Non-Commutative Proof-Nets: perfect matchings, series-parallel orders and Hamiltonian circuits

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