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

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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.

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References

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

    Google Scholar 

  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. 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.

    Google Scholar 

  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.

    Google Scholar 

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

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

  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. 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. 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. 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.

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

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

    Article  Google Scholar 

  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. 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.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

  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.

    Google Scholar 

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Authors and Affiliations

  1. Advanced Software Technology and Mechatronics Research Institute of Kyoto, 17 Chudoji Minami-machi, Shimogyo, 600, Kyoto, Japan

    Chiaki Sakama

  2. Department of Information and Computer Sciences, Toyohashi University of Technology, Tempaku-cho, 441, Toyohashi, Japan

    Katsumi Inoue

Authors
  1. Chiaki Sakama
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  2. Katsumi Inoue
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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

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  • DOI: https://doi.org/10.1007/BF00881915

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