Non-commutative logic I: The multiplicative fragment

Annals of Pure and Applied Logic

Volumn 101, Issue 1, 1999, Pages 29-64

  Abrusci, V Michele ^a   Ruet, Paul ^b  

^a ROMA TRE UNIVERSITY   (Italy)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Linear logic; Order varieties; Proof nets; Sequent calculus

Indexed keywords

EID: 0033570879     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0168-0072(99)00014-7     Document Type: Article

References (20)

1. V.M. Abrusci, Phase semantics and sequent calculus for pure non-commutative classical linear logic, J. Symbolic Logic 56(4) (1991).
2. V.M. Abrusci, Non-commutative proof-nets, LMSLNS, vol. 222, Cambridge University Press, Cambridge 1995.
3. V.M. Abrusci, Lambek calculus, cyclic linear logic, noncommutative linear logic: language and sequent calculus, in: V.M. Abrusci, C. Casadio (Eds.), Proofs and Linguistic Categories, Cooperativa Libraria Universitaria Editrice Bologna, 1997, pp. 21-48.
4. V. Danos, La logique linéaire appliquée à l'étude de divers processus de normalisation (principalement du λ-calcul), Ph.D. Thesis, Université Denis Diderot, Paris 7, 1990.
5. V. Danos, L. Régnier, The structure of multiplicatives, Arch. Math. Logic 28(3) (1989) 181-203.
6. Ph. de Groote, Partially commutative linear logic: sequent calculus and phase semantics, in: V.M. Abrusci, C. Casadio (Eds.), Proofs and Linguistic Categories, Proc. 1996 Roma Workshop. Cooperativa Libraria Universitaria Editrice Bologna, 1996.
7. A. Fleury, La règle d'échange: logique linéaire multiplicative tressée, Ph.D. Thesis, Université Denis Diderot, Paris 7, November 1996.
8. J.-Y. Girard, Linear logic, Theoret. Comput. Sci. 50(1) (1987) 1-102.
9. J.-Y. Girard, Towards a geometry of interaction, Contemp. Math. 92 (1989) 69-108.
10. J.-Y. Girard, On the meaning of logical rules I: syntax vs. semantics, Prépub. Institut de Mathématiques de Luminy, 1998.
11. A. Joyal. Une théorie combinatoire des séries formelles, Adv. Math. 42 (1981) 1-82.
12. J. Lambek, The mathematics of sentence structure, Amer. Math. Mon. 65(3) (1958) 154-170.
13. F. Métayer, Homology of proof nets, Arch. Math. Logic (1994) 33, pp. 169-180.
14. M. Moortgat, Categorial type logics, Handbook of Logic and Language, MIT Press, 1996.
15. V. Novák, Cyclically ordered sets, Czech. Math. J. 32(107) (1982) 460-473.
16. Ch. Retoré, Pomset logic - A non-commutative extension of commutative linear logic, in Proc. Int. Conf. on Typed Lambda-Calculi and Applications, 1997.
17. P. Ruet, Logique non-commutative et programmation concurrente par contraintes, Ph.D. Thesis, Université Denis Diderot, Paris 7, 1997.
18. P. Ruet, Non-commutative logic II: sequent calculus and phase semantics, Preprint (http://www.dcs.ed.ac.uk/∼ruet), 1998.
19. P. Ruet, F. Fages, Concurrent constraint programming and non-commutative logic, in Proc. CSL'97, Annual Conf. EACSL, Lecture Notes in Computer Science, vol. 1414, Springer, Berlin, 1998, pp. 406-423.
20. D.N. Yetter, Quantales and (non-commutative) linear logic, J. Symbolic Logic 55(1) (1990).