Skip to main content Accessibility help

Completeness of MLL proof-nets w.r.t. weak distributivity

  • Jean-Baptiste Joinet (a1)


We examine ‘weak-distributivity’ as a rewriting rule defined on multiplicative proofstructures (so, in particular, on multiplicative proof-nets: MLL). This rewriting does not preserve the type of proof-nets, but does nevertheless preserve their correctness. The specific contribution of this paper, is to give a direct proof of completeness for : starting from a set of simple generators (proof-nets which are a n-ary ⊗ of Ց-ized axioms), any mono-conclusion MLL proof-net can be reached by rewriting (up to ⊗ and Ց associativity and commutativity).



Hide All
[1]Bechet, D., de Groote, P., and Retoré, C., A complete axiomatisation for the inclusion of seriesparallel orders, RTA 97, Lecture Notes in Computer Science, vol. 1232, 1997, pp. 230–240.
[2]Danos, V., La logique linéaire appliquée à l'etude de divers processus de normalisation (principalement du λ-calcul), Ph.D. thesis, Université Paris 7, 06 1990.
[3]Danos, V., Joinet, J-B., and Schellinx, H., Computational isomorphisms in classical logic, Theoretical Computer Science, vol. 294 (2003), no. 3, pp. 353–378.
[4]Danos, V. and Regnier, L., The structure of multiplicatives, Archives for Mathematical Logic, vol. 28 (1995), pp. 181–203.
[5]Devarajan, H., Hughes, D., Plotkin, G., and Pratt, V., Full completeness of the multiplicative linear logic of Chu spaces, Proceedings 14th Annual IEEE Symposium on Logic in Computer Science, LICS '99 (Longo, G., editor), 1999, pp. 234–242.
[6]Girard, J.-Y., Linear logic. Theoretical Computer Science, vol. 50 (1987), pp. 1–102.
[7]Guglielmi, A., A system of interaction and structure, Technical Report WV-02-10, International Center for Computational Logic, Technische Universität Dresden, Germany, 8 November 2004, To appear on ACM Transactions on Computational Logic.
[8]Maieli, R. and Puite, Q., Modularity of proof nets: generating the type of a module, Archive for Mathematical Logic, vol. 44 (2005), no. 2, pp. 167–193.
[9]Retoré, C., Handsome proof-nets: R&B graphs, perfect matchings and Series-Parallel graphs, Technical Report RR-36-52, INRIA, 1999.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed