Skip to main content

Computational and concurrency models of linear logic

  • Conference paper
  • First Online:
  • 142 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 813))

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.Abramsky. Computational interpretation of linear logic. Imperial College Research Report DOC 90/20, 1990.

    Google Scholar 

  2. S.Abramsky, Computational Interpretations of Linear Logic, Theoretical Computer Science, 1992, Special Issue on the 1990 Workshop on Math. Found. Prog. Semantics. To appear.

    Google Scholar 

  3. S.Abramsky and R.Jagadeesan. Games and Full Completeness for Multiplicative Linear Logic. Imperial College Technical Report DOC 92/24, 1992.

    Google Scholar 

  4. A.V.Aho, J.E.Hopcroft, and J.D.Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1976.

    Google Scholar 

  5. A.Asperti. A Logic for Concurrency. Technical Report. Dipartimento di Informatica, Universita di Pisa, 1987.

    Google Scholar 

  6. A.Asperti, G.-L.Ferrari, and R.Gorrieri. Implicative formulae in the’ proofs as computations’ analogy. In Proc. 17-th ACM Symposium on Principles of Programming Languages, San-Francisco, January 1990, p.59–71

    Google Scholar 

  7. J. van Benthem. Language in Action. North-Holland, Amsterdam, 1991.

    Google Scholar 

  8. A.Blass. A game semantics for linear logic. Annals Pure Appl. Logic, 56 (1992) pp.183–220.

    Google Scholar 

  9. A.Brown. Relating Petri Nets to Formulas of Linear Logic. Technical Report. LFCS, Edinburgh, 1989.

    Google Scholar 

  10. P.Degano, J.Meseguer, and U.Montanari. Axiomatizing net computations and processes. In Proc. 4-th Annual IEEE Symposium on Logic in Computer Science, Philadelphia, June 1989, p.175–185.

    Google Scholar 

  11. M.R.Garey and D.S.Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. 1979.

    Google Scholar 

  12. V.Gehlot and C.A.Gunter. Normal process representatives. In Proc. 5-th Annual IEEE Symposium on Logic in Computer Science, Philadelphia, June 1990.

    Google Scholar 

  13. J.-Y.Girard. Linear logic. Theoretical Computer Science, 50:1, 1987, pp.1–102.

    Google Scholar 

  14. J.-Y.Girard and Y.Lafont. Linear logic and lazy computation, Proceedings of TAP-SOFT 87, Springer Lecture Notes in Computer Science n∘257, 1987, pp. 52–66.

    Google Scholar 

  15. J.-Y.Girard. Towards a Geometry of Interaction. Categories in Computer Science and Logic, Contemporary Mathematics 92, AMS 1989, p.69–108.

    Google Scholar 

  16. J.-Y.Girard. Geometry of interaction I: interpretation of system F, Logic Colloquium 88, eds. Ferro & al., North Holland 1989.

    Google Scholar 

  17. J.-Y.Girard. Geometry of Interaction II: deadlock-free algorithms, Proceedings of COLOG'88, eds Martin-Löf & Mints, Springer Lecture Notes in Theoretical Computer Science 417, pp.76–93.

    Google Scholar 

  18. J.-Y.Girard, A.Scedrov, and P.J.Scott, Bounded Linear Logic: A Modular Approach to Polynomial Time Computability, Theoretical Computer Science, 97, 1992, pp.1–66.

    Google Scholar 

  19. J.-Y.Girard. A new constructive logic: classical logic, Mathematical Structures in Computer Science, vol 1.3, 1991.

    Google Scholar 

  20. J.-Y.Girard. On the unity of logic, Annals of Pure and Applied logic, vol. 59.3, 1993.

    Google Scholar 

  21. J.-Y.Girard. Linear logic: a survey, Logic & Algebra of Specification, NATO ASI Series F, 94, eds. Bauer & al., Springer Verlag, 1993.

    Google Scholar 

  22. J.-Y.Girard. Geometry of interaction III: the general case, Proceedings of the Workshop on Linear Logic, MIT Press, (to appear)

    Google Scholar 

  23. C.A.Gunter and V.Gehlot. Nets as Tensor Theories. In Proc. 10-th International Conference on Application and Theory of Petri Nets, Bonn, 1989, p.174–191

    Google Scholar 

  24. D.H.J. de Jongh. Investigations on the intuitionistic propositional calculus. Ph.D.Thesis, University of Wisconsin, Madison, 1968.

    Google Scholar 

  25. M.I.Kanovich. The multiplicative fragment of Linear Logic is NP-complete. Technical Report X-91-13, University of Amsterdam, Institute for Language, Logic, and Information, June 1991

    Google Scholar 

  26. M.I.Kanovich. The Horn fragment of Linear Logic is NP-complete. Technical Report X-91-14, University of Amsterdam, Institute for Language, Logic, and Information, August 1991

    Google Scholar 

  27. M.I.Kanovich. Efficient program synthesis: Semantics, Logic, Complexity. Theoretical Aspects of Computer Software, TACS'91, Japan, Sendai, September 1991. In Lecture Notes in Computer Science, 526, p.615–632

    Google Scholar 

  28. M.I.Kanovich. Fast theorem proving in intuitionistic propositional logic. Centre for Mathematics and Computer Science, Computer Science/Department of Software Technology, Technical Report CS-R9157, December 1991, Amsterdam

    Google Scholar 

  29. M.I.Kanovich. Horn Programming in Linear Logic is NP-complete. In Proc. 7-th Annual IEEE Symposium on Logic in Computer Science, Santa Cruz, June 1992, pp.200–210

    Google Scholar 

  30. M.I.Kanovich. Complexity of LL fragments. Email message. 14 July 1992.

    Google Scholar 

  31. M.I.Kanovich. The complexity of Horn Fragments of Linear Logic, Annals Pure Appl. Logic, (1993) (to appear)

    Google Scholar 

  32. M.I.Kanovich. Linear Logic as a Logic of Computations, Annals Pure Appl. Logic, 67 (1994).

    Google Scholar 

  33. M.I.Kanovich. Simulating Linear Logic in 1-Only Linear Logic. CNRS, Laboratoire de Mathématiques Discrètes, Prétirage n∘ 94-02, January 1994, 81 p. Available by anonymous ftp from host ftp.lmd.univ-mrs.fr and the file pub/kanovich/unit-only.dvi.

    Google Scholar 

  34. M.I.Kanovich. The Independent Basis of Neutral Formulas in Linear Logic. CNRS, Laboratoire de Mathématiques Discrètes, Prétirage n∘ 94-08, March 1994, 43 p. Available by anonymous ftp from host ftp.lmd.univ-mrs.fr and the file pub/kanovich/neutrals.dvi.

    Google Scholar 

  35. Y.Lafont and T.Streicher. Games semantics for linear logic. In Proc. 6-th Annual IEEE Symposium on Logic in Computer Science, 43–51, Amsterdam, July 1991.

    Google Scholar 

  36. J.Lambek. The mathematics of sentence structure. American Mathematical Monthly, 65(3):154–170, 1958.

    Google Scholar 

  37. P.Lincoln, J.Mitchell, A.Scedrov, and N.Shancar. Decision Problems for Propositional Linear Logic. Technical Report SRI-CSL-90-08, CSL, SRI International, August 1990.

    Google Scholar 

  38. P.Lincoln, J.Mitchell, A.Scedrov, and N.Shankar. Decision Problems for Propositional Linear Logic. In Proc. 31st IEEE Symp. on Foundations of Computer Science, 662–671, 1990.

    Google Scholar 

  39. P.Lincoln, J.Mitchell, A.Scedrov, and N.Shankar. Decision Problems for Propositional Linear Logic. Annals Pure Appl. Logic, 56 (1992) pp. 239–311.

    Google Scholar 

  40. P.Lincoln, A.Scedrov, and N.Shancar. Linearizing Intuitionistic Implication. In Proc. 6-th Annual IEEE Symposium on Logic in Computer Science, 51–62, Amsterdam, July 1991.

    Google Scholar 

  41. P.Lincoln and T.Winkler. Constant multiplicative Linear Logic is NP-complete. Draft, 1992.

    Google Scholar 

  42. N.Marti-Oliet and J.Mesequer. From Petri Nets to Linear Logic. In: Springer LNCS 389, ed. by D.R.Pitt et al., 1989, p.313–340

    Google Scholar 

  43. E.Mayr and A.Meyer. The complexity of the word problems for commutative semigroups and polynomial ideals. Advances in Mathematics, 46, 305–329, 1982.

    Google Scholar 

  44. E.Mayr, An algorithm for the general Petri net reachability problem. SIAM J.Comput., 13, N 3, 441–460, 1984.

    Google Scholar 

  45. J.Meseguer and U.Montanari. Petri Nets Are Monoids. Research Report SRI-CSL-88-3, SRI International, Menlo Park, January 1988.

    Google Scholar 

  46. M.Minsky. Recursive unsolvability of Post's problem of’ tag’ and other topics in the theory of Turing machines. Annals of Mathematics, 74:3:437–455, 1961.

    Google Scholar 

  47. I.Nishimura. On formulas of one propositional variable in intuitionistic propositional calculus. J.Symb.Logic, 25, 327–331, 1960.

    Google Scholar 

  48. V.R.Pratt, Event spaces and their linear logic, In AMAST'91: Algebraic Methodology and Software Technology, Iowa City, 1991, Workshops in Computing, 1–23, Springer-Verlag, 1992.

    Google Scholar 

  49. R.Statman, Intuitionistic propositional logic is Polynomial-Space complete. Theoret. Computer Sci., 9, 67–72, 1979.

    Google Scholar 

  50. A.S.Troelstra, Lectures on Linear Logic, CSLI Lecture Notes No. 29, Center for the Study of Language and Information, Stanford University, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Anil Nerode Yu. V. Matiyasevich

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kanovich, M.I. (1994). Computational and concurrency models of linear logic. In: Nerode, A., Matiyasevich, Y.V. (eds) Logical Foundations of Computer Science. LFCS 1994. Lecture Notes in Computer Science, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58140-5_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-58140-5_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58140-6

  • Online ISBN: 978-3-540-48442-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics