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Deduction with supernormal defaults

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Nonmonotonic and Inductive Logic (NIL 1991)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 659))

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Abstract

In this paper we consider supernormal defaults [Poo88] with a strict partial order defining their priorities [Bre91]. We investigate their relation to minimal or preferential entailment and show that the semantics given in [Bre91] has to be modified in order to be equivalent to a preferential model approach. Concering the multiple extension problem, we introduce the careful view as an alternative to the credulous and skeptical one, which is needed to handle the generalized closed world assumption [Min82] within this framework.

Given this “declaritive semantics” of such default theories, we will present a deduction algorithm for query answering. Compared to other approaches, the algorithm is quite efficient and general. Especially, it is able to generate disjunctive answers, to support the credulous, skeptical and careful view; and to cut fruitless search paths early. In order to check the applicability of defaults as soon as possible, we introduce the notion of a partial extension.

This work was partially supported by the CEC under the ESPRIT BRA Working Group IS-CORE (Information Systems — COrectness and REusability), coordinated by Amilcar Sernadas.

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References

  1. C. E. Alchourrón, D. Makinson: Ilierarchies of regulations and their logic. In R. Hilpinen (ed.), New Studies in Deontic Logic, 125–148, D. Reidel Publishing Company, 1981.

    Google Scholar 

  2. A. B. Baker, M. L. Ginsberg: A theorem prover for prioritized circumscription. In Proc. 11th International Joint Conf. on Artificial Intelligence (IJCAI), 463–467, 1989.

    Google Scholar 

  3. S. Brass, U. W. Lipeck: Specifying closed world assumptions for logic databases. In J. Demetrovics, B. Thalheim (eds.), 2nd Symposium on Mathematical Fundamentals of Database Systems (MFDBS'89), 68–84, LNCS 364, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  4. S. Brass, U. W. Lipeck: Semantics of inheritance in logical object specifications. In C. Delobel, M. Kifer, Y. Masunaga (eds.), Deductive and Object-Oriented Databases, 2nd Int. Conf. (DOOD'91), 411–430, LNCS 566, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  5. S. Brass, U. W. Lipeck: Generalized bottom-up query evaluation. In Advances in Database Technology — EDBT'92, 3rd Int. Conf., 88–103, LNCS 580, Springer-Verlag, 1992.

    Google Scholar 

  6. S. Brass: Beginnings of a theory of general database completions. In S. Abiteboul, P. C. Kanellakis (eds.), Third International Conference on Database Theory (ICDT'90), 349–363, LNCS 470, Springer-Verlag, Berlin, 1990.

    Google Scholar 

  7. G. Brewka: Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press, Cambridge, 1991.

    Google Scholar 

  8. S. Brass, M. Ryan, U. W. Lipeck: Hierarchical defaults in specifications. In G. Saake, A. Sernadas (eds.), Information Systems — Correctness and Reusability, Workshop IS-CORE '91, 179–201, Informatik-Bericht 91-03, TU Braunschweig, 1991.

    Google Scholar 

  9. F. Bry: Query evaluation in recursive databases: bottom-up and top-down reconciled. Data & Knowledge Engineering 5 (1990), 289–312.

    Google Scholar 

  10. G. Bossu, P. Siegel: Saturation, non-monotonic reasoning and the closed-world assumption. Artificial Intelligence 25 (1985), 13–63.

    Google Scholar 

  11. C.-L. Chang, R. C.-T. Lee: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.

    Google Scholar 

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

    Google Scholar 

  13. D. M. Gabbay: Theoretical foundations for non-monotonic reasoning in expert systems. In K. R. Apt (ed.), Logics and Models of Concurrent Systems, 439–457, Springer, Berlin, 1985.

    Google Scholar 

  14. M. L. Ginsberg: A circumscriptive theorem prover. Artificial Intelligence 39 (1989), 209–230.

    Google Scholar 

  15. M. Gelfond, H. Przymusinska: Negation as failure: Careful closure procedure. Artificial Intelligence 30 (1986), 273–287.

    Google Scholar 

  16. M. Gelfond, H. Przymusinska, T. Przymusinski: The extended closed world assumption and its relationship to parallel circumscription. In Proc. of the Fifth ACM SIGACT-SIGMOD Symp. on Principles of Database Syst. (PODS'86), 133–139, 1986.

    Google Scholar 

  17. C. C. Green: Theorem-proving by resolution as a basis for question-answering systems. In B. Meltzer, D. Michie (eds.), Machine Intelligence, volume 4, 183–205. Edinburgh University Press, 1969.

    Google Scholar 

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

    Google Scholar 

  19. V. Lifschitz: Closed-world databases and circumscription. Artificial Intelligence 27 (1985), 229–235.

    Google Scholar 

  20. V. Lifschitz: Computing circumscription. In Proc. 9th International Joint Conference on Artificial Intelligence (IJCAI), 121–127, Los Angeles, 1985.

    Google Scholar 

  21. J.W. Lloyd: Foundations of Logic Programming, 2nd edition. Springer-Verlag, Berlin, 1987.

    Google Scholar 

  22. D. Makinson: General theory of cumulative inference. In Non-Monotonic Reasoning (2nd International Workshop), 1–18, LNAI 346, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  23. D. Makinson: General patterns in nonmonotonic reasoning. In D. Gabbay (ed.), Handbook of Logic in Artificial Intelligence and Logic Programming, volume 2. Oxford University Press, 1992. 79 pages.

    Google Scholar 

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

    Google Scholar 

  25. J. McCarthy: Applications of circumscription to formalizing common-sense knowledge. Artificial Intelligence 28 (1986), 86–116.

    Google Scholar 

  26. J. Minker: On indefinite databases and the closed world assumption. In D. W. Loveland (ed.), 6th Conference on Automated Deduction, 292–308, LNCS 138, Springer-Verlag, Berlin, 1982.

    Google Scholar 

  27. J. Minker, D. Perlis: Computing protected circumscription. The Journal of Logic Programming 2 (1985), 235–249.

    Google Scholar 

  28. D. Poole: A logical framework for default reasoning. Artificial Intelligence 36 (1988), 27–47.

    Google Scholar 

  29. T. C. Przymusinski: On the declarative semantics of deductive databases and logic programs. In J. Minker (ed.), Foundations of Deductive Databases and Logic Programming, 193–216, Morgan Kaufmann Publishers, Los-Altos (Calif.), 1988.

    Google Scholar 

  30. T. C. Przymusinski: An algorithm to compute circumscription. Artificial Intelligence 38 (1989), 49–73.

    Google Scholar 

  31. R. Reiter: On closed world data bases. In I.I. Gallaire, J. Minker (eds.), Logic and Data Bases, 55–76, Plenum, New York, 1978.

    Google Scholar 

  32. R. Reiter: A logic for default reasoning. Artificial Intelligence 13 (1980), 81–132.

    Google Scholar 

  33. M. Ryan: Defaults and revision in structured theories. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'91), 362–373, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, FG Datenbanken und Informationssysteme, Universität Hannover, Lange Laube 22, D-W-3000, Hannover 1, Fed. Rep. Germany

    Stefan Brass

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  1. Stefan Brass
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Gerhard Brewka Klaus P. Jantke Peter H. Schmitt

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© 1993 Springer-Verlag Berlin Heidelberg

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Brass, S. (1993). Deduction with supernormal defaults. In: Brewka, G., Jantke, K.P., Schmitt, P.H. (eds) Nonmonotonic and Inductive Logic. NIL 1991. Lecture Notes in Computer Science, vol 659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030392

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  • DOI: https://doi.org/10.1007/BFb0030392

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56433-1

  • Online ISBN: 978-3-540-47557-6

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