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

Sylvain Pogodalla 1 Christian Retoré 2
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 SIGNES - Linguistic signs, grammar and meaning: computational logic for natural language
INRIA Futurs, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Université Bordeaux Montaigne, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : 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.
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Sylvain Pogodalla, Christian Retoré. Handsome Non-Commutative Proof-Nets: perfect matchings, series-parallel orders and Hamiltonian circuits. [Research Report] RR-5409, INRIA. 2004, pp.25. ⟨inria-00071248⟩

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