Modal Linear Logic

  • Dimitry A. Archangelsky
  • Mikhail A. Taitslin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 620)


In this paper we continue our study of Girard's Linear Logic and introduce a new Linear Logic with modalities. Our logic describes not only consumption, but presence of resources as well. It describes transformation of resources not only for the single point but for some net, where supplies can be sent from one object to another one using interfaces. We introduce a new semantics and a new calculus for this logic and prove the completeness theorem for this calculus in respect to our semantics.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J.-Y Girard, Linear Logic. Theoretical computer science, 50:1–102, 1987CrossRefGoogle Scholar
  2. [2]
    J.-Y Girard, La logique linéaire. Pour La Science, Edition Francaise de Scientific American, 150: 74–85, 1990.Google Scholar
  3. [3]
    S. Abramsky, Intuitionistic Linear Logic Considered as a Programming Language. Preprint, 1990.Google Scholar
  4. [4]
    Y. Lafont, The linear abstract machine. Theoretical computer science, 59:157–180, 1988.CrossRefGoogle Scholar
  5. [5]
    Y. Lafont, Interaction nets. Proc. 17th ACM Symp. on Principles of Programming Languages, 95–108,1990.Google Scholar
  6. [6]
    P. Lincoln, J. Mitchell, A. Scerdov, N. Shankar, Decision Problems for Propositional Linear Logic. In Proc. 31th IEEE Symp. Found Comput. Sci., 662–671, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Dimitry A. Archangelsky
    • 1
  • Mikhail A. Taitslin
    • 1
  1. 1.TverRussia

Personalised recommendations