Non-commutative logic II: Sequent calculus and phase semantics

Mathematical Structures in Computer Science

Volumn 10, Issue 2, 2000, Pages 277-312

  Ruet†, Paul ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003306730     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129599003084     Document Type: Article

References (17)

1. Abrusci, V. M. and Ruet, P. (2000) Non-commutative logic I: the multiplicative fragment. Annals Pure Appl. Logic 101 (1) 29–64.
2. Andreoli, J.-M. (1992) Logic programming with focusing proofs in linear logic. J. Logic and Comp. 2(3).
3. Bechet, D., de Groote, P. and Retore, Ch. (1997) A complete axiomatisation for the inclusion of series-parallel orders. Proc. Int. Conf. on Rewriting Techniques and Applications. Springer-Verlag Lecture Notes in Computer Science.
4. de Groote, P. Partially commutative linear logic : sequent calculus and phase semantics. In: Abrusci, V. M. and Casadio, C. (eds.) Proofs and Linguistic Categories, Proc. 1996 Roma Workshop, Cooperativa Libraria Universitaria Editrice Bologna.
5. Demaille, A. (1999) Logique lineaires hybrides et leurs modalites: theories et applications, Ph.D. thesis, Ec. Nat. Sup. Telecommunications.
6. Fuchs, L. (1963) Partially ordered algebraic systems, Pergamon Press.
7. Girard, J.-Y. (1987) Linear logic. Theoret. Comp. Sci. 50 (1) 1–102.
8. Girard, J.-Y. (1989) Towards a geometry of interaction. Contemp. Math. 92 69–108.
9. Girard, J.-Y. (1995) Linear logic: its syntax and semantics. In: Advances in Linear Logic, London Mathematical Society Lecture Note Series, 222, Cambridge University Press, 1–42.
10. Girard, J.-Y. (1999) On the meaning of logical rules I: syntax vs. semantics. In: Berger, U. and Schwichtenberg, H. (eds.) Computational Logic, NATO Series F 165, Springer-Verlag.
11. Lafont, Y. (1997) The finite model property for various fragments of linear logic. J. Symb. Logic 62 (4) 1202–1208.
12. Lambek, J. (1958) The mathematics of sentence structure. Amer. Math. Monthly 65 (3) 154–170.
13. Mohring, R. (1989) Computationally tractable classes of ordered sets, ASI Series 222, NATO.
14. Novak, V. (1982) Cyclically ordered sets. Czech. Math. J. 32 (107) 460–473.
15. Okada, M. (1994) Girard’s phase semantics and a higher-order cut-elimination proof. Preprint Institut de Mathematiques de Luminy.
16. P. Ruet. (1997) Logique non-commutative et programmation concurrente par (P. ) contraintes, Ph.D. thesis, Universite Denis Diderot, Paris 7.
17. Yetter, D.N. (1990) Quantales and (non-commutative) linear logic. J. Symb. Logic 55 (1).