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Static semantics for normal and disjunctive logic programs

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Abstract

In this paper, we propose a newsemantic framework for disjunctive logic programming by introducingstatic expansions of disjunctive programs. The class of static expansions extends both the classes of stable, well-founded and stationary models of normal programs and the class of minimal models of positive disjunctive programs. Any static expansion of a programP provides the corresponding semantics forP consisting of the set of all sentences logically implied by the expansion. We show that among all static expansions of a disjunctive programP there is always theleast static expansion, which we call thestatic completion ¯P ofP. The static completion¯P can be defined as the least fixed point of a naturalminimal model operator and can be constructed by means of a simpleiterative procedure. The semantics defined by the static completion¯P is called thestatic semantics ofP. It coincides with the set of sentences that are true inall static expansions ofP. For normal programs, it coincides with the well-founded semantics. The class of static expansions represents a semantic framework which differs significantly from the other semantics proposed recently for disjunctive programs and databases. It is also defined for a much broader class of programs.

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References

  1. K. Apt, H. Balir and A. Walker, Towards a theory of declarative knowledge, in:Foundations of Deductive Databases and Logic Programming, ed. J. Minker (Morgan Kaufmann, Los Altos, CA, 1988) pp. 89–142.

    Google Scholar 

  2. J.J. Alferes and L.M. Pereira, On logic program semantics with two kinds of negation, in:Int. Joint Conf. and Symp. on Logic Programming, ed. K. Apt (MIT Press, 1992) pp. 574–588.

  3. J. Alferes, L. Periera and T.C. Przymusinski, Belief revision in logic programming and non-monotonic reasoning, University of Lisbon and University of California at Riverside (in preparation).

  4. J. Alferes, L. Pereira and T.C. Przymusinski, Strong and explicit negation in non-monotonic reasoning and logic programming, University of Lisbon and University of California at Riverside (in preparation).

  5. C. Baral, J. Lobo and J. Minker, Generalized disjunctive well-founded semantics for logic programs: Declarative semantics, in:Proc. 5th Int. Symp. on Methodology for Intelligent Systems, eds. Z. Ras and Emrich, ACM SIGMOD-SIGACT-SIGART (North-Holland, 1989).

  6. C. Baral, J. Lobo and J. Minker, Generalized well-founded semantics for logic programs,10th Int. Conf. on Automated Deduction, West Germany (1990).

  7. J. Dix, Classifying semantics of logic programs, in:Proc. 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, Washington, DC, eds. A. Nerode, W. Marek and V.S. Subrahmanian (MIT Press, Cambridge, MA, 1991) pp. 166–180.

    Google Scholar 

  8. J. Dix, Classifying semantics of disjunctive logic programs, in:Logic Programming: Proc. 1992 Joint Int. Conf. and Symp., ed. K. Apt (MIT Press, 1992) pp. 798–812.

  9. M. Gelfond, On stratified autoepistemic theories,Proc. AAAI-87 (American Association for Artificial Intelligence/Morgan Kaufmann, Los Altos, CA, 1987) pp. 207–211.

    Google Scholar 

  10. M. Gelfond and V. Lifschitz, The stable model semantics for logic programming,Proc. 5th Logic Programming Symp. (Association for Logic Programming/MIT Press, Cambridge, MA, 1988) pp. 1070–1080.

    Google Scholar 

  11. M. Gelfond and V. Lifschitz, Logic programs with classical negation,Proc. 7th Int. Logic Programming Conf. Jerusalem, Israel (Association for Logic Programming/MIT Press, Cambridge, MA, 1990) pp. 579–597.

    Google Scholar 

  12. G. Gottlob, The complexity of propositional default reasoning under the stationary sematics, Technical Report CD-TR-92/42, Institut für Informationssysteme, Technische Universität, A-1040 Wien, Austria (1992).

    Google Scholar 

  13. M. Gelfond, H. Przymusinska and T. Przymusinski, On the relationship between circumscription and negation as failure, J. Artificial Intelligence 38(1989)75–94.

    Google Scholar 

  14. J. Horty, R. Thomason and D. Touretzky, A skeptical theory of inheritance in non-monotonic semantic nets,Proc. AAAI-87 (American Association for Artificial Intelligence/Morgan Kaufmann, Los Altos, CA, 1987).

    Google Scholar 

  15. J. Bobo, J. Minker and A. Rajasekar,Foundations of Disjunctive Logic Programming (MIT Press, Cambridge, MA, 1992).

    Google Scholar 

  16. J. McCarthy, Circumscription — a form of non-monotonic reasoning, J. Artificial Intelligence 13(1980)27–39.

    Google Scholar 

  17. J. Minker, On indefinite data bases and the closed world assumption,Proc. 6th Conf. on Automated Deduction (Springer, New York, 1982) pp. 292–308.

    Google Scholar 

  18. R.C. Moore, Semantic considerations on non-monotonic logic, J. Artificial Intelligence 25(1985)75–94.

    Google Scholar 

  19. W. Marek and M. Truszczynski,Non-monotonic Logic (Springer, 1994).

  20. L.M. Pereira and J.J. Alferes, Well founded semantics for logic programs with explicit negation, in:European Conf. on Artificial Intelligence, ed. B. Neumann (Wiley, 1992) pp. 102–106.

  21. L.M. Pereira, J.J. Alferes and J.A. Aparicio, Well founded semantics with explicit negation and default theory, Research Report, New University of Lisbon (1992).

  22. H. Przymusinska and T.C. Przymusinki, Semantic issues in deductive databases and logic programs, in:Formal Techniques in Artificial Intelligence, ed. R. Banerji (North-Holland, Amsterdam, 1990) pp. 321–367.

    Google Scholar 

  23. T.C. Przymusinki, On the declarative semantics of stratified deductive databases and log programs, in:Foundations of Deductive and Logic Programming, ed. J. Minker (Morgan Kaufmann, Los Altos, CA, 1988) pp. 193–216.

    Google Scholar 

  24. T.C. Przymusinki, The well-founded semantics coincides with the three-valued stable semantics, Fundamenta Informaticae 13(1990)445–464.

    Google Scholar 

  25. T.C. Przymusinski, Autoepistemic logics of closed beliefs and logic programming, in:Proc. 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, Washington, DC, eds. A. Nerode, W. Marek and V.S. Subrahmanian (MIT Press, Cambridge, MA, 1991) pp. 3–20.

    Google Scholar 

  26. T.C. Przymusinski, Semantics of disjunctive logic programs and deductive databases, in:Proc. 2nd Int. Conf. on Deductive and Object-Oriented Databases DOOD '91, Munich, Germany, eds. C. Delobel, M. Kifer and Y. Masunaga (Springer, 1991) pp. 85–107.

  27. T.C. Przymusinski, Stable semantics for disjunctive programs, New Generation Comp. J. 9(1991)401–424. Extended abstract appeared in: Extended stable semantics for normal and disjunctive logic programs,Proc. 7th Int. Logic Programming Conf., Jerusalem (MIT Press, Cambridge, MA, 1990) pp. 459–477.

    Google Scholar 

  28. T.C. Przymusinski, Well-founded completions of logic programs,Proc. 8th Int. Logic Programming Conf. Paris, France (Association for Logic Programming/MIT Press, Cambridge, MA, 1991) pp. 726–744.

    Google Scholar 

  29. T.C. Przymusinski, Autoepistemic logic of knowledge and beliefs, Technical Report, University of California at Riverside (in preparation).

  30. T.C. Przymusinski, A knowledge representation framework based on autoepistemic logic of minimal beliefs,Proc. 12th National Conf. on Artificial Intelligence, AAAI-94, Seattle, Washington (American Association for Artificial Intelligence/Morgan Kaufmann, Los Altos, CA, 1994) pp. 952–959.

    Google Scholar 

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

    Google Scholar 

  32. K. Ross, The well founded semantics for disjunctive logic programs,Proc. 1st Int. Conf. on Deductive and Object Oriented Databases (1989) pp. 352–369.

  33. K. Ross and R. Topor, Inferring negative information from disjunctive databases, J. Autom. Reasoning 4(1988)397–424.

    Google Scholar 

  34. A. Van Gelder, Negation as failure using tight derivations for general logic programs, J. Logic Program. 6(1989)109–133. Preliminary versions appeared in3rd IEEE Symp. on Logic Programming (1986) andFoundations of Deductive Databases and Logic Programming, ed. J. Minker (Morgan Kaufmann, 1988).

    Google Scholar 

  35. A. Van Gelder, K.A. Ross and J.S. Schlipf, The well-founded semantics for general logic programs, J. ACM (to appear). Preliminary abstract appeared in7th ACM Symp. on Principles of Database Systems (1988), pp. 221–230.

  36. L. Yuan and J. You, Autoepistemic circumscription and logic programming, Technical Report TR92-18, Department of Computing Science, University of Alberta (1992), to appear in J. Autom. Reasoning.

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Authors and Affiliations

  1. Department of Computer Science, University of California, 92521, Riverside, CA, USA

    Teodor C. Przymusinski

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  1. Teodor C. Przymusinski
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Dedicated to Jack Minker

Partially supported by the National Science Foundation grant # IRI-9313061.

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Przymusinski, T.C. Static semantics for normal and disjunctive logic programs. Ann Math Artif Intell 14, 323–357 (1995). https://doi.org/10.1007/BF01530826

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