Petri nets as models of linear logic

  • Uffe Engberg
  • Glynn Winskel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 431)


The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Asp87]
    Andrea Asperti. A Logic for Concurrency. manuscript, November 1987.Google Scholar
  2. [AV88]
    Samson Abramsky and Steve Vickers. Linear Process Logic. Notes by Steve Vickers, 1988.Google Scholar
  3. [Bro89a]
    Carolyn Brown. Relating Petri Nets to Formulae of Linear Logic. Technical Report ECS LFCS 89-87, University of Edinburgh, 1989.Google Scholar
  4. [Bro89b]
    Carolyn Brown. Petri Nets as Quantales. Technical Report ECS LFCS 89–96, University of Edinburgh, 1989.Google Scholar
  5. [GG89]
    Carl Gunter and Vijay Gehlot. A Proof-Theoretic Operational Semantics for True Concurrency. Preliminary Report, 1989.Google Scholar
  6. [Gir87]
    Jean-Yves Girard. Linear Logic. Theoretical Computer Science, 50(1):1–102, 1987.CrossRefGoogle Scholar
  7. [GL87]
    Jean-Yves Girard and Yves Lafont. Linear Logic and Lazy Computation. In Proc. TAPSOFT 87 (Pisa), vol. 2, pages 52–66. Springer-Verlag (LNCS 250), 1987.Google Scholar
  8. [Laf88]
    Yves Lafont. The Linear Abstract Machine. Theoretical Computer Science, 59:157–180, 1988.CrossRefGoogle Scholar
  9. [MOM89]
    Narciso Martí-Oliet and José Meseguer. From Petri Nets to Linear Logic. In Category Theory and Computer Science, Manchester, UK. Springer-Verlag (LNCS 389), 1989.Google Scholar
  10. [Rei85]
    Wolfgang Reising. Petri Nets, An Introduction, volume 4 of EATCS Monogaphs on Theoretical Computer Science. Springer-Verlag, 1985.Google Scholar
  11. [Ros]
    Kimmo I. Rosenthal. A Note on Girard Quantales. To appaear in: Cah. de Top. et G. D.Google Scholar
  12. [Sam]
    G. Sambin. Manuscript reported to us by Per Martin-Löf.Google Scholar
  13. [Yet]
    D. Yetter. Quantales and Non-Commutative Linear Logic. (preprint).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Uffe Engberg
    • 1
  • Glynn Winskel
    • 1
  1. 1.Computer Science DepartmentAarhus UniversityAarhus CDenmark

Personalised recommendations