An Effective Bottom-Up Semantics for First-Order Linear Logic Programs

  • Marco Bozzano
  • Giorgio Delzanno
  • Maurizio Martelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2024)


We study the connection between algorithmic techniques for symbolic model checking [ACJT96,FS98,AJ99], and declarative and op- erational aspects of linear logic programming [And92,AP90]. Specifically, we show that the construction used to decide verification problems for Timed Petri Nets [AJ99] can be used to define a new fixpoint semantics for the fragment of linear logic called LO [AP90]. The fixpoint semantics is based on an effective T P operator. As an alternative to traditional top-down approaches [And92,AP90,APC93], the effective fixpoint operator can be used to define a bottom-up evaluation procedure for first-order linear logic programs.


Operational Semantic Proof System Atomic Formula Linear Logic Symbolic Model Check 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ACJT96]
    P. A. Abdulla, K. Cerāns, B. Jonsson and Y.-K. Tsay. General Decidability Theorems for Infinite-State Systems. In Proc. of LICS 96, pages 313–321, 1996.Google Scholar
  2. [AJ99]
    P. A. Abdulla, and B. Jonsson. Ensuring Completeness of Symbolic Verification Methods for Infinite-State Systems. To appear in Theoretical Computer Science, 1999.Google Scholar
  3. [AN00]
    P. A. Abdulla, and A. Nylen. Better is Better than Well: On Efficient Verification of Infinite-State Systems. In Proc. LICS’2000, pages 132–140, 2000.Google Scholar
  4. [And92]
    J. M. Andreoli. Logic Programming with Focusing proofs in Linear Logic. Journal of Logic and Computation, 2(3):297–347, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [AP90]
    J. M. Andreoli and R. Pareschi. Linear Objects: Logical Processes with Built-In Inheritance. In Proc. of ICLP’90, pages 495–510, 1990.Google Scholar
  6. [APC93]
    J. M. Andreoli, R. Pareschi and T. Castagnetti. Abstract Interpretation of Linear Logic Programming. In Proc. of ILPS’93, pages 295–314, 1993.Google Scholar
  7. [BDM00]
    M. Bozzano, G. Delzanno, and M. Martelli. A Bottom-up semantics for Linear Logic Programs. In Proc. of PPDP 2000, pages 92–102, 2000.Google Scholar
  8. [BDM00a]
    M. Bozzano, G. Delzanno, and M. Martelli. An Effective Bottom-Up Semantics for First-Order Linear Logic Programs and its Relationship with Decidability Results for Timed Petri Nets. Technical Report, DISI, UniVersità di Genova, Decemeber 2000.Google Scholar
  9. [Cer95]
    I. Cervesato. Petri Nets and Linear Logic: a Case Study for Logic Programming. In Proc. of GULP-PRODE’95, pages 313–318, 1995.Google Scholar
  10. [DP99]
    G. Delzanno and A. Podelski. Model Checking in CLP. In Proc. of TACAS’99, LNCS 1579, pages 223–239, 1999.Google Scholar
  11. [FLMP93]
    M. Falaschi and G. Levi and M. Martelli and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102(1):86–113, 1993.CrossRefMathSciNetGoogle Scholar
  12. [FS98]
    A. Finkel and P. Schnoebelen. Well-structured Transition Systems Everywhere! Technical Report LSV-98-4, Laboratoire Spécification et Vérification, ENS Cachan, 1998. To appear in Theoretical Computer Science, 1999.Google Scholar
  13. [Fri00]
    L. Fribourg. Constraint logic programming applied to model checking. In Proc. LOPSTR’99, pages 31–42, 2000.Google Scholar
  14. [GDL95]
    M. Gabbrielli, M. G. Dore and G. Levi. Observable Semantics for Constraint Logic Programs. Journal of Logic and Computation, 5(2): 133–171, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [Gir87]
    J. Y. Girard. Linear Logic. Theoretical Computer Science, 50:1–102, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [HM94]
    J. S. Hodas and D. Miller. Logic Programming in a Fragment of Intuitionistic Linear Logic. Information and Computation, 110(2):327–365, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [HW98]
    J. Harland and M. Winiko. Making Logic Programs Reactive. In Proc. of JICSLP’98 Workshop Dynamics’98, pages 43–58, 1998.Google Scholar
  18. [JM94]
    J. Jaffar and M. J. Maher. Constraint Logic Programming: A Survey. Journal of Logic Programming, 19-20:503–582, 1994.CrossRefMathSciNetGoogle Scholar
  19. [Kan94]
    M. I. Kanovich. Petri Nets, Horn Programs, Linear Logic, and Vector Games. In Proc TACS. ’94, pages 642–666, 1994.Google Scholar
  20. [KMM+97]
    Y. Kesten, O. Maler, M. Marcus, A. Pnueli, E. Shahar. Symbolic Model Checking with Rich Assertional Languages. In Proc. CAV ’97, pages 424–435, 1997.Google Scholar
  21. [Kop95]
    A. P. Kopylov. Propositional Linear Logic with Weakening is Decidable. In Proc. LICS 95, pages 496–504, 1995.Google Scholar
  22. [Llo87]
    J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987.Google Scholar
  23. [MM91]
    N. Martì-Oliet, J. Meseguer. From Petri Nets to Linear Logic. Mathematcal Structures in Computer Science 1(1):69–101, 1991.zbMATHCrossRefGoogle Scholar
  24. [Mil96]
    D. Miller. Forum: A Multiple-Conclusion Specification Logic. Theoretical Computer Science, 165(1):201–232, 1996.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marco Bozzano
    • 1
  • Giorgio Delzanno
    • 1
  • Maurizio Martelli
    • 1
  1. 1.Dipartimento di Informatica e Scienze dell’InformazioneUniversitá di GenovaItaly

Personalised recommendations