Skip to main content
Log in

Well-founded semantics and stratification for ordered logic programs

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

Abstract

This paper present an extension of traditional logic programming, called ordered logic (OL) programming, to support classical negation as well as constructs from the object-oriented paradigm. In particular, such an extension allows to cope with the notions of object, multiple inheritance and non-monotonic reasoning.

The contribution of the work is mainly twofold. First, a rich wellfounded semantics for ordered logic programs is defined. Second, an efficient method for the well-founded model computation of a meaningful class of ordered logic programs, called stratified programs, is provided.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Apt, K., Bair, H. and Walker, A., “Towards a Theory of Declarative Knowledge,”Foundations of Deductive Databases and Logic Programming (Minker, J., ed.), Morgan Kaufman, Los Altos, pp. 89–148, 1987.

    Google Scholar 

  2. Ait-Kaci, H. and Nasr, R., “LOGIN: A Logic Programming Language with Built-in Inheritance,”Journal Logic Programming, 3, 3, Oct. 1986.

  3. Ahlsen, M., Johannesson, P., Laenens, E., Leone, N., Rullo, P., Rossi, G., Staes, F., Tarantino, L., Van Beirendonck, L., Van Cadsand, F., Van Sant, W., Van Slembroeck, J., Verdonk, B. and Vermeir, D. (ed.), “The KIWIS Knowledge Base Management System,” inProceedings of the 3rd Int. Conference CAiSE’ 91, Trondheim, Norway, May 1991.

  4. Baral, C., Lobo, J. and Minker, J., “Generalized Well-Founded Semantics for Logic Programs,”Research Report, University of Maryland, 1990.

  5. Bancilhon, F., Maier, D., Sagiv, Y. and Ullman, J. D., “Magic Sets and Other Strange Ways to Implement Logic Programs,”Proceedings of the 5th ACM SIGMODSIGACT Symp. on Principles of Database Systems, 1986.

  6. Beeri, C., Naqvi, S., Ramakrishnan, R., Shmueli, O, and Tsur, S., “Sets and Negation in a Logic Database Language (LDLI),”Proc. Sixth Annual ACM Symposium on Principles of Database Systems, pp. 21–37, 1987.

  7. Balbin, I. and Ramamohanarao, K., “A Generalization of the Differential Approach to Recursive Query Evaluation,”Journal of Logic Programming 4, 3, pp. 259–262, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  8. Beeri, C. and Ramakrishnan, R., “On the Power of Magic,” inProc. 6th ACM SIGMOD-SIGACT Symp. on Principles of Databases Systems, pp. 269–283, 1987.

  9. Blair, H. and Subrahmanian, V.S., “Paraconsistent Logic Programming,”Theoretical Computer Science, 68, pp. 135–154, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  10. Baral, C. and Subrahmanian, V.S., “Stable and Extension Class Theory for Logic Programs and Default Logics,”Research Report, University of Maryland, 1990.

  11. Chen, W. and Warren, D.J., “C-logic for Complex Objects,”Proc. ACM SIGACT-SIGMOD-SIGART Symp on Principles of Database Systems, March 1989.

  12. Conery, J.S., “Object Oriented Programming with First Order Logic,”Technical Report, CIS-TR-87-09, Univ. of Oregon, 1987.

  13. Gelfond, M. and Lifschitz, V. “Logic Programs with Classical Negation,”Proc. of 7th ICLP, Jerusalem, pp. 579–597, 1990.

  14. Greco, S., Leone, N. and Rullo, P., “COMPLEX: An Object-Oriented Logic Programming System,”IEEE Transaction on Data and Knowledge Engineering, August 1992.

  15. Greco, S. and Saccà, D., “Negative Logic Programs,”Proc. of North American Logic Programming Conference, 1990.

  16. Geert, P. and Vermeir, D., “Credulous and Autoepistemic Reasoning Using Ordered Logic,”Proc. of the 1st Int. Workshop on Logic Programming and Nonmonotonic Reasoning, Washington, July 1991.

  17. Kifer, M. and Lausen, G., “F-logic: A Higher-Order Language for Reasoning About Objects, Inheritance, and Scheme,”Proc. of the ACM SIGMOD Int. Conf. on the Management of Data, Portland, Oregon, 1989.

  18. Kifer, M. Lausen, G. and Wu, J., “Logical Foundation of Object-Oriented and Frame-Based Languages,”Technical Report, 90/14, Dept. of Computer Science, New York State Univ. at Stony Brook, June 1990.

  19. Kowalski, R.A. and Sadri, F., “Logic Programs with Exceptions,”Proc. of 7th ICLP, Jerusalem, pp 598–616, 1990.

  20. Kuper, G. M., “Logic Programming with Sets,”Journal of Computer and System Sciences, 41, 1, pp. 44–64, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  21. Laenens, E., “Foundations of Ordered Logic,”Ph.D. thesis, Univ. of Antwerp, 1990.

  22. Lloyd, J. W., inFoundations of Logic Programming, Springer-Verlag, 1987.

  23. Leone, N., Mecchia, A., Rossi, G. and Rullo, P., “Revised Design Documentation of the Basic Language Machine,”Technical Report, BLM5/91, ESPRIT Project P2424 KIWIS, September 1991.

  24. Leone, N. and Rossi, G., “Well-Founded Semantics for Ordered Logic Programs,”Proc. of GULP’91, Pisa, Italy, 1991.

  25. Leone, N., Rossi, G. and Rullo, P., “Design Documentation of the Basic Language Machine,”Technical Report, BLM4/90, ESPRIT Project P2424 KIWIS, December 1990.

  26. Leone, N. and Rullo, P., “Stable Model Semantics and Its Computation for Ordered Logic Programs,”Proceedings ECAI 92-10th European Conference on AI, Vienna, Austria, August 3–7 1992.

  27. Leone, N. and Rullo, P., “On the Relation of Ordered Logic to Nonmonotonic Formalisms,”Research Report, CRAI, 1992.

  28. Laenens, E., Saccàa, D. and Vermeir, D., “Extending Logic Programming,”Proc. of ACM SIGMOD, May 1990.

  29. Laenens, E. and Vermeir, D., “A Fixpoint Semantics for Ordered Logic,”Journal of Logic and Computation 1, 2, pp. 159–185, December 1990.

    Article  MATH  MathSciNet  Google Scholar 

  30. Laenens, E. and Vermeir, D., “KIWIS: Advanced Knowledge-Base Environments for Large Database Systems,”Proc. of the PARBASE 90 Conference, IEEE Computer Society Press, 1990.

  31. Laenens, E., Verdonk, B., Vermeir, D. and Cuyt, A., “A Logic for Objects and Inheritance,”Proc. of the Advanced Database Symposium, Kyoto, Japan, 1989.

  32. Naqvi, S. and Tsur, S.,A Logical Data Language for Data and Knowledge Bases, Computer Science Press, New York, 1988.

    Google Scholar 

  33. Roussel, P.,Prolog, Manuel de Reference et de Utilisation, Groupe Intelligence Artificielle, Universite Aix-Marseille II, 1975.

  34. Przymusinsky, T., “Well-Founded Semantics Coincides with Three-Valued Stable Semantics,”Fundamenta Informaticae, XIII, IOS Press, pp. 445–463, 1990.

    Google Scholar 

  35. Saccà, D. and Zaniolo, C., “Implementing Recursive Logic Queries with Function Symbols,”MCC Technical Report, DB-065-86, February 20 1986.

  36. Saccà, D. and Zaniolo, C., “The Generalized Counting Method of Recursive Logic Queries for Databases,”Theoretical Computer Science, 62, pp. 187–220, Nov. 1989.

    Article  Google Scholar 

  37. Saccà, D. and Zaniolo, C., “Partial Model, Stable Models and Non-Determinism in Logic Programs with Negation,”Proc. ACM Symp. on Principles of Database Systems, 1990.

  38. Tarsky, A., “A Lattice Theoretical Fixpoint Theorem and Its Application,”Pacific Journal of Mathematics, 5, pp. 285–309, 1955.

    MathSciNet  Google Scholar 

  39. Tarjan, R., “Depth-First Search and Linear Graph Algorithm,”SIAM Journal of Computing, 1, 2, June 1972.

  40. Touretzky, D.S.,The Mathematics of Inheritance Systems, Pitman, London, 1986.

    MATH  Google Scholar 

  41. Van Gelder, A., “The Alternating Fixpoint of Logic Programs with Negation,”Proc. ACM Symp. on Principles of Database Systems, 1989.

  42. Van Gelder A., Ross, K. and Schlipf, J.S., “Unfounded Sets and Well-Founded Semantics for General Logic Programs,”Proc. ACM SIGMOD-SIGACT Symp. on Principles of Database Systems, pp. 221–230, March 1988.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Leone.

Additional information

Research partially supported byEEC in the framework of ESPRIT II project EP2424 “KIWIS”.

Part of this work has been developed while the author was with CRAI.

Nicola Leone, Ph. D: He received the Doctoral degree in Mathematics from the University of Calabria (Italy). In June 1986 he joined CRAI (an industrial consortium for information technology research and application at Rende, Italy), where he worked as computer scientist researcher until December 1992. During this period he was leader of the CRAI team in an ESPRIT project and in several national projects. Since January 1993 he has been Lecturer of Computer Science at the University of Calabria. His research interests are in the areas of deductive databases and knowledge bases. In particular, his current research activities are focused on non-monotonic reasoning, efficient query evaluation, updates, and on combining logic programming with the object-oriented paradigm. He is author of over 30 papers published in scientific journals, books and conference proceedings.

Giuseppe Rossi: He received in 1992 a three years grant for young computer scientists. In 1985 he joined CRAI, a research and application center in Informatics located at Rende (Italy), where presently he is a senior researcher. He has been active in the area of data and knowledge base design and implementation; in particular he was involved in two large ESPRIT projects (namely, KIWI and KIWIS) for the exploitation of the logic and object-oriented paradigms within a novel knowledge based system. Since 1992 he is also working on some knowledge modeling issues within the CRAI speech recognition group.

About this article

Cite this article

Leone, N., Rossi, G. Well-founded semantics and stratification for ordered logic programs. New Gener Comput 12, 91–121 (1993). https://doi.org/10.1007/BF03038273

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03038273

Keywords

Navigation