Skip to main content
SpringerLink
Log in

Compositional model-theoretic semantics for logic programs

  • Regular Papers
  • Published:
New Generation Computing Aims and scope Submit manuscript

Abstract

We present a compositional model-theoretic semantics for logic programs, where the composition of programs is modelled by the composition of the admissible Herbrand models of the programs. An Herbrand model is admissible if it is supported by the assumption of a set of hypotheses. On one hand, the hypotheses supporting a model correspond to an open interpretation of the program intended to capture possible compositions with other programs. On the other hand, admissible models provide a natural model-theory for a form of hypothetical reasoning, called abduction. The application of admissibel models to programs with negation is discussed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Apt, K. R., “Logic Programming,” inHandbook of Theoretical Computer Science (J. van Leeuwen, ed.), Vol. B, Elsevier, pp. 493–574, 1990.

  2. Apt, K. R. and van Emden, M. H., “Contributions to the Theory of Logic Programming,”Journal of the ACM, 29, 3, pp. 841–862, 1982.

    Article  MATH  Google Scholar 

  3. Bossi, A., Gabbrielli, M., Levi, G., and Meo, M. C., “Contribution to the Semantics of Open Logic Programs,” inProceedings of FGCS92 (ICOT, ed.), pp. 570–580, Ohmsha, 1992.

  4. Brogi, A., Lamma, E., Mancarella, P., and Mello, P., “Abductive Reasoning in a Multi-Theory Framework,” inTrends in Artificial Intelligence (S. Gaglio, ed.),Proceedings of the Second Congress of the Italian Association for Artificial Intelligence, Lecture Notes in Artificial Intelligences, 549, Palermo, Springer-Verlag, pp. 137–146, 1991.

    Google Scholar 

  5. Brogi, A., Lamma, E., Mancarella, P., and Mello, P., “Normal Logic Programs as Open Positive Programs” inProceedings 1992 Joint International Conference on Logic Programming (K. R. Apt and J. Minker, eds.) the MIT Press, 1992.

  6. Brogi, A., Lamma, E., and Mello, P., “Open Logic Theories,” inProceedings of Second Workshop on Extensions of Logic Programming, Lectures Notes in Artificial Intelligence, H.-H. Eriksson, P. Krueger, and P. Schroeder-Heister, eds., Kista, Springer-Verlag, Jan. 1991.

    Google Scholar 

  7. Brogi, A., Mancarella, P., Pedreschi, D., and Turini, F., “Composition Operators for Logic Theories,” inComputational Logic (J. W. Lloyd, ed.),Symposium Proceedings, Springer-Verlag, 596, pp. 73–88 Brussels, pp. 117–134, Nov. 1990.

  8. Charniak, E. and McDermott, D.,Introduction to Artificial Intelligence, Addison-Wesely, 1985.

  9. Clark, K., “Negation as Failure,” inLogic and Data Bases (H. Gallaire and J. Minker, eds.), Plenum, pp. 293–322, 1978.

  10. Dung, P. M., “Negation as Hypothesis: An Abductive Foundation for Logic Programming,” inProc. 8th International Conference on Logic Programming (K. Furukawa, ed.), The MIT Press, pp. 3–17, 1991.

  11. Eshgi, K. and Kowalski, R. A., “Abduction Compared with Negation by Failure,” inProc. Sixth International Conference on Logic Programming (G. Levi and M. Martelli, eds.), The MIT Press, pp. 234–254, 1989.

  12. Gaifman, H. and Shapiro, E., “Fully Abstract Compositional Semantics for Logic Programs,” inProc. Sixteenth POPL, pp. 134–142, 1989.

  13. Gelfond, M. and Lifschitz, V., “The Stable Models Semantics for Logic Programs,” inProc. Fifth International Conference on Logic Programming (R. A. Kowalski and K. A. Bowen, eds.), The MIT Press, pp. 1070–1080, 1988.

  14. Kakas, A. C. and Mancarella, P., “Generalized Stable Models: a Semantics for Abduction,” inProceedings of 9th European Conference on Artificial Intelligence (L. Carlucci Aiello, ed.) Pitman, pp. 385–391, 1990.

  15. Kowalski, R. A., “Problems and Promises of Computational Logic,” inComputational Logic, Symposium Proceedings (J. W. Lloyd, ed.), Springer-Verlag, Brussels, pp. 1–36, Nov. 1990.

    Google Scholar 

  16. Lloyd, J. W.,Foundations of Logic Programming, second edition, Springer-Verlag, 1987.

  17. Mancarella, P. and Pedreschi, D., “An Algebra of Logic Programs,” inProc. Fifth International Conference on Logic Programming (R. A. Kowalski and K. A. Bowen, eds.), The MIT Press, pp. 1006–1023, 1988.

  18. Mancarella, P., Pedreschi, D., Rondinelli, M., and Tagliatti, M., “Algebraic Properties of a Class of Logic Programs,” inProc. NACLP (S. Debray and M. Hermenegildo, eds.), The MIT Press, pp. 23–49, 1990.

  19. Miller, D., “A Logical Analysis of Modules in Logic Programming,”Journal of Logic Programming, 6, pp. 79–108, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  20. Monteiro, L. and Porto, A., “Contextual Logic Programming,” inProc. Sixth International Conference on Logic Programming (G. Levi and M. Martelli, eds.), The MIT Press, pp. 284–302, 1989.

  21. O’Keefe, R., “Towards an Algebra for Constructing Logic Prograams,” inProceedings of IEEE Symposium on Logic Programming (J. Cohen and J. Conery, eds.), IEEE Computer Society Press, pp. 152–160, 1985.

  22. Poole, D., “Compiling a Default Reasoning System into Prolog,”New Generation Computing, 9, 1, pp. 3–38, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  23. Poole, D. L., “A Logical Framework for Default Reasoning,”Artificial Intelligence, 36, pp. 27–47, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  24. Przymusinski, T. C., “Extended Stable Semantics for Normal and Disjunctive Programs,” inProc. 7th International Conference on Logic Programming (D. H. D. Warren and P. Szeredi, eds.), The MIT Press, pp. 459–477, 1990.

  25. Przymusinski, T. C., “Semantics of Disjunctive Logic Programs and Deductive Databases,” inProc. DOOD91 (C. Delobel, M. Kifer and Y. Masunaga, eds.), Springer-Verlag, pp. 85–107, 1991.

  26. Reiter, R., “On Closed World Data Bases,” inLogic and Data Bases (Gallaire and J. Minker, eds.), Plenum, pp. 293–322, 1978.

  27. Sacca, D. and Zaniolo, C., “Stable Models and Nondeterminism in Logic Programs with Negation,” inProc. 9th ACM Symp. on Principles of Database Systems, ACM, pp. 205–217, 1990.

  28. Sacca, D. and Zaniolo, C., “Partial Models and Three-Valued Models in Logic Programs with Negation,” inProc. Workshop on Logic Programming and Non-Monotonic Reasoning, The MIT Press, pp. 87–101, 1991.

  29. van Emden, M. H. and Kowalski, R. A., “The Semantics of Predicate Logic as a Programming Language,”Journal of the ACM, 23, 4, pp. 733–742, 1976.

    Article  MATH  Google Scholar 

  30. Van Gelder, A., Ross, K. A., and Schlipf, J. S., “Unfounded Sets and the Well-Founded Semantics of General Logic Programs,” inProc. ACM SIGMODSIGACT Symp. on Principles of Database Systems, ACM, pp. 221–230, 1988.

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125, Pisa, Italy

    Antonio Brogi

  2. DEIS, Università di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Evelina Lamma & Paola Mello

Authors
  1. Antonio Brogi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evelina Lamma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paola Mello
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Antonio Brogi: Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125 Pisa, ItalyResearch interests: Programming Language Design and Semantics, Logic Programming and Artificial Intelligence

Evelina Lamma, Ph. D.: Associate Professor, The University of Udine, (Present Address) Dipartimento di Electronica, Informatica e Sistemistica, Università di Bologna, Viale Risorgimento 2, 40136 Bologna, ItalyResearch interests: Programming Languages and Knowledge Representation, with particular reference to Logic Languages and their extentions.

Paola Mello, Ph. D.: Associate Professor, Dipartimento di Electronica, Informatica e Sistemistica, Università di Bologna, Viale Risorgimento 2, 40136 Bologna, ItalyResearch interests: Programming Languages and Knowledge Representation, with particular reference to theoretical and practical aspects of extentions of Logic Programming

About this article

Cite this article

Brogi, A., Lamma, E. & Mello, P. Compositional model-theoretic semantics for logic programs. New Gener Comput 11, 1–21 (1992). https://doi.org/10.1007/BF03037525

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03037525

Keywords

Search

Navigation