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A Correct Logic Programming Computation of Default Logic Extensions

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Abstract

We present a method of representing some classes of default theories as normal logic programs. The main point is that the standart semantics (i.e., SLDNF-resolution) computes answer substitutions that correspond exactly to the extensions of the represented default theory. This means that we give a correct implementation of default logic. We explain the steps of constructing a logic program LogProg(P, D) from a given default theory (P, D), give some examples, and derive soundness and completeness results.

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References

  1. Antoniou, G. and Sperschneider, V.: Computing extensions of nonmonotonic logics, in Proc. 4th Scandinavian Conference on Artificial Intelligence, IOS Press, 1993, pp. 20–29.

  2. Antoniou, G. and Langetepe, E.: Soundness and completeness of a logic programming approach to default logic, in Proc. AAAI-94,AAAI Press, 1994, pp. 934–939.

  3. Antoniou, G. and Langetepe, E.: Applying SLD-resolution to a class of non-Horn logic programs, J. IGPL2(2) (1994), 229–241.

    Google Scholar 

  4. Bidoit, N. and Froidevaux, C.: General logic databases and programs: Default logic semantics and stratification, J. Information and Computation 94(1991), 15–54.

    Google Scholar 

  5. Bidoit, N. and Froidevaux, C.: Negation by default and unstratifiable logic programs, Theoretical Computer Science 78(1991), 85–112.

    Google Scholar 

  6. Froidevaux, C.: Taxonomic default theory, in Proc. European Conference on Artificial Intelligence, Brighton, 1986.

  7. Gelfond, M. and Lifschitz, V.: The stable model semantics for logic programming, in Proc. 5th Int. Conference/Symposium on Logic Programming, 1988, pp. 1070–1080.

  8. Lloyd, J. W.: Foundations of Logic Programming, 2nd edn, Springer-Verlag, 1987.

  9. 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 

  10. Marek, W. and Truszcynski, M.: Stable semantics for logic programs and default theories, in Proc. North American Conference on Logic Programming, 1989, pp. 243–256.

  11. Pereira, L. M. and Nerode, A.: Logic programming and non-monotonic reasoning, Proceedings of the 2nd International Workshop, MIT Press, 1993.

  12. Poole, D.: A logical framework for default reasoning, Artificial Intelligence 36(1988).

  13. Przymusinski, T. C.: On the relationship between nonmonotonic reasoning and logic programming, Proc. AAAI-88, 1988.

  14. Przymusinski, T. C.: Autoepistemic logic of closed beliefs and logic programming, Proc. 1st International Workshop on Logic Programming and Non-Monotonic Reasoning, 1991.

  15. Reiter, R.: A logic for default reasoning, Artificial Intelligence 13, 1980.

  16. Schlechta, K.: Directly sceptical inheritance cannot capture the intersection of extensions, Proc. GMD Workshop on Nonmonotonic Reasoning, GMD, 1989.

  17. Sperschneider, V. and Antoniou, G.: Logic: A Foundation for Computer Science,Addison-Wesley, 1991.

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Antoniou, G., Langetepe, E. A Correct Logic Programming Computation of Default Logic Extensions. Journal of Automated Reasoning 18, 25–46 (1997). https://doi.org/10.1023/A:1005771523328

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