Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

An alternative approach to the semantics of disjunctive logic programs and deductive databases

  • 52 Accesses

  • 48 Citations

Abstract

In this paper, we study a new semantics of logic programming and deductive databases. Thepossible model semantics is introduced as a declarative semantics of disjunctive logic programs. The possible model semantics is an alternative theoretical framework to the classical minimal model semantics and provides a flexible inference mechanism for inferring negation in disjunctive logic programs. We also present a proof procedure for the possible model semantics and show that the possible model semantics has an advantage from the computational complexity point of view.

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

References

  1. 1.

    Apt, K. R., Blair, H. A. and Walker, A.: Towards a theory of declarative knowledge, in J. Minker (ed.),Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann, 1988, pp. 89–148.

  2. 2.

    Baral, C., Lobo, J. and Minker, J.: Generalized disjunctive well-founded semantics for logic programs,Ann. Mathematics and Artificial Intelligence 5 (1992), 89–132.

  3. 3.

    Bancilhon, F. and Ramakrishnan, R.: Performance evaluation of data intensive logic programs, in J. Minker (ed.),Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann, 1988, pp. 439–517.

  4. 4.

    Chan, E. P. F.: A possible world semantics for disjunctive databases,IEEE Trans. on Knowledge and Data Engineering 5(2) (1993), 282–292. Preliminary version in: Research Report CS-89-47, Dept. of Computer Science, Univ. of Waterloo, 1989.

  5. 5.

    Clark, K. L.: Negation as failure, in H. Gallaire and J. Minker (eds.),Logic and Data Bases, Plenum, New York, 1978, pp. 293–322.

  6. 6.

    Decker, H.: Foundations of first-order databases, Research Report, Siemens, 1992. Preliminary version inProc. 2nd Int. Workshop on the Deductive Approach to Information Systems and Databases, Universitat Politecnica de Catalunya, Report de Recerca LSI/91/30, 1991, pp. 149–173.

  7. 7.

    Decker, H. and Casamayor, J. C.: Sustained models and sustained answers in first order databases,Proc. 4th Int. Workshop on the Deductive Approach to Information Systems and Databases, 1993.

  8. 8.

    Dix, J.: Classifying semantics of disjunctive logic programs,Proc. Joint Int. Conf. and Symp. on Logic Programming, MIT Press, 1992, pp. 798–812.

  9. 9.

    Dung, P. M.: Negation as failure for disjunctive logic programming,Proc. ILPS'91 Post-Conference Workshop on Disjunctive Logic Programs, 1991.

  10. 10.

    Eiter, T. and Gottlob, G.: Complexity aspects of various semantics for disjunctive databases,Proc. 12th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 1993, pp. 158–167.

  11. 11.

    Eiter, T., Gottlob, G. and Gurevich, Y.: Curb Your Theory!: A circumscriptive approach for inclusive interpretation of disjunctive information,Proc. IJCAI-93, Morgan Kaufmann, 1993, pp. 634–639.

  12. 12.

    Eshghi, K. and Kowalski, R. A.: Abduction compared with negation by failure,Proc. 6th Int. Conf. on Logic Programming, MIT Press, 1989, pp. 234–254.

  13. 13.

    Fernandez, J. A., Lobo, J., Minker, J. and Subrahmanian, V. S.: Disjunctive LP + integrity constraints = stable model semantics,Ann. Mathematics and Artificial Intelligence 8(3&4) (1993), 449–474.

  14. 14.

    Gelfond, M. and Lifschitz, V.: The Stable model semantics for logic programming,Proc. 5th Int. Conf. and Symp. on Logic Programming, MIT Press, 1988, pp. 1070–1080.

  15. 15.

    Gelfond, M. and Lifschitz, V.: Classical negation in logic programs and disjunctive databases,New Generation Computing 9(3&4) (1991), 365–385.

  16. 16.

    Gelfond, M.: Strong introspection,Proc. AAAI-91, MIT Press, 1991, pp. 386–391.

  17. 17.

    Inoue, K., Koshimura, M. and Hasegawa, R.: Embedding negation as failure into a model generation theorem prover,Proc. 11th Int. Conf. on Automated Deducation, Lecture Notes in Artificial Intelligence 607, Springer-Verlag, 1992, 400–415.

  18. 18.

    Inoue, K. and Sakama, C.: Transforming abductive logic programs to disjunctive programs,Proc. 10th Int. Conf. on Logic Programming, MIT Press, 1993, pp. 335–353.

  19. 19.

    Inoue, K. and Sakama, C.: On positive occurrences of negation as failure,Proc. 4th Int. Conf. on Principles of Knowledge Representation and Reasoning, Morgan Kaufmann, 1994, pp. 293–304.

  20. 20.

    Kraus, S., Lehmann, D. and Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics,Artificial Intelligence 44(1) (1990), 167–207.

  21. 21.

    Lobo, J., Minker, J. and Rajasekar, A.:Foundations of Disjunctive Logic Programming, MIT Press, 1992.

  22. 22.

    Manthey, R. and Bry, F.: SATCHMO: A theorem prover implemented in Prolog,Proc. 9th Int. Conf. on Automated Deducation, Lecture Notes in Computer Science 310, Springer-Verlag, 1988, pp. 415–434.

  23. 23.

    McCarthy, J.: Circumscription — a form of nonmonotonic reasoning,Artificial Intelligence 13(1&2) (1980), 27–39.

  24. 24.

    Minker, J.: On indefinite data bases and the closed world assumption,Proc. 6th Int. Conf. on Automated Deduction, Lecture Notes in Computer Science 138, Springer-Verlag, 1982, pp. 292–308.

  25. 25.

    Marek, W. and Subrahmanian, V. S.: The relationship between stable, supported, default and autoepistemic semantics for general logic programs,Theoretical Computer Science 103 (1992), 365–386.

  26. 26.

    Marek, W. and Truszczynski, M.: Autoepistemic logic,J. ACM 38(3) (1991), 588–619.

  27. 27.

    Marek, W. and Truszczynski, M.: Computing intersection of autoepistemic expansions,Proc. 1st Int. Workshop on Logic Programming and Nonmonotonic Reasoning, MIT Press, 1991, 37–50.

  28. 28.

    Przymusinski, T. C.: On the declarative semantics of deductive databases and logic programs, in J. Minker (ed.),Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann, 1988, pp. 193–216.

  29. 29.

    Przymusinski, T. C.: Stable semantics for disjunctive programs,New Generation Computing 9(3&4) (1991), 401–424.

  30. 30.

    Przymusinski, T. C.: Semantics of disjunctive logic programs and deductive databases,Proc. 2nd Int. Conf. on Deductive and Object-Oriented Databases, Lecture Notes in Computer Science 566, Springer-Verlag, 1991, pp. 85–107.

  31. 31.

    Reiter, R.: On closed world databases, in H. Gallaire and J. Minker (eds.),Logic and Data Bases, Plenum, New York, 1978, pp. 55–76.

  32. 32.

    Rajasekar, A., Lobo, J. and Minker, J.: Weak generalized closed world assumption,J. Automated Reasoning 5 (1989), 293–307.

  33. 33.

    Ross, K.: The well founded semantics for disjunctive logic programs,Proc. 1st Int. Conf. on Deductive and Object-Oriented Databases, North-Holland, 1989, pp. 385–401.

  34. 34.

    Ross, K. A. and Topor, R. W.: Inferring negative information from disjunctive databases,J. Automated Reasoning 4(2) (1988), 397–424.

  35. 35.

    Sakama, C.: Possible model semantics for disjunctive databases,Proc. 1st Int. Conf. on Deductive and Object-Oriented Databases, North-Holland, 1989, pp. 369–383.

  36. 36.

    Sakama, C. and Inoue, K.: Negation in disjunctive logic programs,Proc. 10th Int. Conf. on Logic Programming, MIT Press, 1993, pp. 703–719.

  37. 37.

    Sakama, C. and Inoue, K.: On the equivalence between disjunctive and abductive logic programs,Proc. 11th Int. Conf. on Logic Programming, MIT Press, 1994, pp. 489–503.

  38. 38.

    Sato, T.: Completed logic programs and their consistency,J. Logic Programming 9(1), 1990, pp. 33–44.

  39. 39.

    Schlipf, J. S.: Formalizing a logic for logic programming.Ann. Mathematics and Artificial Intelligence 5 (1992), 279–302.

  40. 40.

    Van Emden, M. H. and Kowalski, R. A.: The semantics of predicate logic as a programming language,J. ACM 23(4) (1976), 733–742.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sakama, C., Inoue, K. An alternative approach to the semantics of disjunctive logic programs and deductive databases. J Autom Reasoning 13, 145–172 (1994). https://doi.org/10.1007/BF00881915

Download citation

Key words

  • disjunctive logic programs
  • possible model semantics
  • closed world assumption
  • model generation procedure