A game semantics foundation for logic programming

Extended abstract
  • Roberto Di Cosmo
  • Jean-Vincent Loddo
  • Stephane Nicolet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1490)


We introduce a semantics of Logic Programming based on an classical Game Theory, which is proven to be sound and complete w.r.t. the traditional operational semantics and Negation as Failure. This game semantics is based on an abstract reformulation of classical results about two player games, and allows a very simple characterization of the solution set of a logic program in terms of approximations of the value of the game associated to it, which can also be used to capture in a very simple way the traditional “negation as failure” extensions. This approach to semantics also opens the way to a better understanding of the mechanisms at work in parallel implementations of logic programs and in the operational semantics of logic programs with negative goals.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aumann and Hart (eds). Handbook of Game Theory with Economic Applications. 1992.Google Scholar
  2. [2]
    Samson Abramsky and Rhada Jagadeesan. Games and full completeness for multiplicative linear logic. The Journal of Symbolic Logic, 59(2):543–574, 1994.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Krzysztof Apt. From Logic Programming to Prolog. Prentice Hall, 1997.Google Scholar
  4. [4]
    A. Bossi, M. Gabbrielli, G. Levi, and M. Martelli. The s-semantics approach: Theory and applications. Journal of Logic Programming, 19–20:149–197, 1994.MathSciNetCrossRefGoogle Scholar
  5. [5]
    A. Blass. A game semantics for linear logic. Annals of Pure and Applied Logic, 56:pages 183–220, 1992.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    M.G. Brockington. A taxonomy of parallel game-tree search algorithms. Journal of the International Computer Chess Association, 19(3):162–174, 1996.Google Scholar
  7. [7]
    P.L. Curien and H. Herbelin. Computing with abstract bohm trees. 1996.Google Scholar
  8. [8]
    Levi Comici and Meo. Compositionality of SLD-derivations and their abstractions. ILPS, 1995.Google Scholar
  9. [9]
    K. Doets. Levationis Laus. Journal of Logic Computation, 3(5):pages 487–516, 1993.MATHMathSciNetGoogle Scholar
  10. [10]
    E. Eder. Properties of substitutions and unifications. Journal of Symbolic Computation, (1):31–46, 1985.Google Scholar
  11. [11]
    A. Joyal. Free lattices, communication and money games. Proceedings of the 10th International Congress of Logic, Methodology, and Philosophy of Science, 1995.Google Scholar
  12. [12]
    F. Lamarche. Game semantics for full prepositional linear logic. LICS, pages 464–473, 1995.Google Scholar
  13. [13]
    Jean Loddo and Stéphane Nicolet. Theorie des jeux et langages de programmation. Technical report TR-98-01, ENS, 45, Rue d'Ulm, 1998.Google Scholar
  14. [14]
    G. Levi and F. Patricelli. Prolog: Linguaggio Applicazioni ed Implementazioni. Scuola Superiore G. Reiss Romoli, 1993.Google Scholar
  15. [15]
    C. Palamidessi. Algebraic properties of idempotent substitutions, ICALP, LNCS, 443, 1990.Google Scholar
  16. [16]
    V. Danos P. Baillot and T. Ehrhard. Believe it or not, AJM's games model is a model of classical linear logic. LICS, pages 68–75, 1997.Google Scholar
  17. [17]
    J. von Neumann. Zur Theorie der Gesellschaftsspiele. Mathaematische Annalen, (100):195–320, 1928.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Roberto Di Cosmo
    • 1
  • Jean-Vincent Loddo
    • 1
  • Stephane Nicolet
    • 1
  1. 1.DMI-LIENS Ecole Normale SupérieureParisFrance

Personalised recommendations