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On Open Defaults

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Computational Logic

Part of the book series: ESPRIT Basic Research Series ((ESPRIT BASIC))

Abstract

In Reiter’s default logic, the parameters of a default are treated as metavariables for ground terms. We propose an alternative definition of an extension for a default theory, which handles parameters as genuine object variables. The new form of default logic may be preferable when the domain closure assumption is not postulated. It stands in a particularly simple relation to circumscription. Like circumscription, it can be viewed as a syntactic transformation of formulas of higher order logic.

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References

  1. Nicole Bidoit and Christine Froidevaux. Negation by default and nonstratifiable logic programs. Technical Report 437, Université Paris XI, September 1988.

    Google Scholar 

  2. David Etherington. Relating default logic and circumscription. In Proc. IJCAI-87, pages 489–494, 1987.

    Google Scholar 

  3. David Etherington. A semantics for default logic. In Proc. IJCAI-87, pages 495–498, 1987.

    Google Scholar 

  4. Michael Gelfond and Vladimir Lifschitz. Compiling circumscriptive theories into logic programs. In Michael Reinfrank, Johan de Kleer, Matthew Ginsberg, and Erik Sandewall, editors, Non-Monotonic Reasoning: 2nd International Workshop (Lecture Notes in Artificial Intelligence 346), pages 74–99. Springer-Verlag, 1989.

    Google Scholar 

  5. Michael Gelfond and Vladimir Lifschitz. Logic programs with classical negation. In David Warren and Peter Szeredi, editors, Logic Programming: Proc. of the Seventh Int’l Conf., pages 579–597, 1990.

    Google Scholar 

  6. Ramiro Guerreiro and Marco Casanova. An alternative semantics for default logic. Preprint, The Third International Workshop on Nonmonotonic Reasoning, South Lake Tahoe, 1990.

    Google Scholar 

  7. Kurt Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343–382, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kurt Konolige. On the relation between autoepistemic logic and circumscription. In Proc. of IJCAI-89, pages 1213–1218, 1989.

    Google Scholar 

  9. Robert Kowalski and Fariba Sadri. Logic programs with exceptions. In David Warren and Peter Szeredi, editors, Logic Programming: Proc. of the Seventh Int’l Conf., pages 598–613, 1990.

    Google Scholar 

  10. Hector Levesque. All I know: a study in autoepistemic logic. Artificial Intelligence, 42(2,3):263–310, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  11. Vladimir Lifschitz. Computing circumscription. In Proc. of IJCAI-85, pages 121–127, 1985.

    Google Scholar 

  12. Vladimir Lifschitz. Benchmark problems for formal non-monotonic reasoning, version 2.00. In Michael Reinfrank, Johan de Kleer, Matthew Ginsberg, and Erik Sandewall, editors, Non-Monotonic Reasoning: 2nd International Workshop (Lecture Notes in Artificial Intelligence 346), pages 202–219. Springer-Verlag, 1989.

    Google Scholar 

  13. Vladimir Lifschitz. Between circumscription and autoepistemic logic. In Ronald Brachman, Hector Levesque, and Raymond Reiter, editors, Proc. of the First Int’l Conf. on Principles of Knowledge Representation and Reasoning, pages 235–244, 1989.

    Google Scholar 

  14. Wiktor Marek and Miroslaw Truszczyński. Relating autoepistemic and default logic. In Ronald Brachman, Hector Levesque, and Raymond Reiter, editors, Proc. of the First Int’l Conf. on Principles of Knowledge Representation and Reasoning, pages 276–288, 1989.

    Google Scholar 

  15. Wiktor Marek and Miroslaw Truszczyński. Modal logic for default reasoning. To appear, 1990.

    Google Scholar 

  16. John McCarthy. Circumscription—a form of non-monotonic reasoning. Artificial Intelligence, 13(1, 2):27–39,171–172, April 1980.

    Article  MathSciNet  MATH  Google Scholar 

  17. John McCarthy. Applications of circumscription to formalizing common sense knowledge. Artificial Intelligence, 26(3):89–116, 1986.

    Article  MathSciNet  Google Scholar 

  18. Drew McDermott and Jon Doyle. Nonmonotonic logic I. Artificial Intelligence, 13(l,2):41–72, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  19. Drew McDermott. Nonmonotonic logic II: Nonmonotonic modal theories. Journal of the ACM, 29(l):33–57, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  20. David Poole. Fixed predicates in default reasoning. Manuscript, 1987.

    Google Scholar 

  21. David Poole. Variables in hypotheses. In Proc. IJCAI-87, pages 905–908, 1987.

    Google Scholar 

  22. Teodor Przymusinski. On the declarative and procedural semantics of logic programs. Journal of Automated Reasoning, 5:167–205, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  23. Raymond Reiter. A logic for default reasoning. Artificial Intelligence, 13(1,2):81–132, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  24. Raymond Reiter. On integrity constraints. In Moshe Vardi, editor, Theoretical Aspects of Reasoning about Knowledge: Proc. of the Second Conf., pages 97–111, 1988.

    Google Scholar 

  25. Grigori Shvarts. Autoepistemic modal logics. In Rohit Parikh, editor, Theoretical Aspects of Reasoning about Knowledge: Proc. of the Third Conf., pages 97–110, 1990.

    Google Scholar 

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© 1990 ECSC — EEC — EAEC, Brussels — Luxembourg

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Lifschitz, V. (1990). On Open Defaults. In: Lloyd, J.W. (eds) Computational Logic. ESPRIT Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76274-1_3

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  • DOI: https://doi.org/10.1007/978-3-642-76274-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76276-5

  • Online ISBN: 978-3-642-76274-1

  • eBook Packages: Springer Book Archive

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