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Nonmonotonic reasoning with multiple belief sets

  • Joeri Engelfriet
  • Heinrich Herre
  • Jan Treur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1085)

Abstract

In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze multiple belief sets in an abstract setting. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selective inference operations connected to belief set operators and which are used to choose one of the possible views.

Keywords

nonmonotonic inference knowledge representation belief sets 

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References

  1. [ABW88]
    Apt, K.R., Blair, H.A., Walker, A.: Towards a Theory of Declarative Knowledge, in: Minker, J. (ed), Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann, 1988, pp. 89–142Google Scholar
  2. [AGM85]
    Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the Logic of Theory Change: Partial Meet Contraction and Revision Functions; Journal of Symbolic Logic 50, 510–530 (1985)Google Scholar
  3. [Be89]
    Besnard, P.: An Introduction to Default Logic; Berlin, Springer-Verlag, 1989Google Scholar
  4. [Br91]
    Brewka, G.: Nonmonotonic Reasoning: Logical Foundations of Commonsense, Cambridge University Press, 1991Google Scholar
  5. [Br94]
    Brewka, G.: Adding Priorities and Specificity to Default Logic; in: C. MacNish, D. Pearce, L.M. Pereira (eds.) Logics in Artificial Intelligence, JELIA'94, Springer Verlag, 1994Google Scholar
  6. [Di94]
    Dietrich, J.: Deductive Bases of Nonmonotonic Inference Operations: NTZ-Report,7/94, University of Leipzig, 1994Google Scholar
  7. [DH94]
    Dietrich, J., H. Herre: Outline of Nonmonotonic Model Theory, NTZ-Report, 5/94, University of Leipzig, 1994Google Scholar
  8. [EHT95]
    Engelfriet, J., H. Herre, J. Treur: Nonmonotonic Belief State Frames and Reasoning Frames, in: C. Froidevaux, J. Kohlas (eds.), Proc. ECSQARU'95, Lecture Notes in AI, vol. 946, Springer Verlag, 1995, pp. 189–196Google Scholar
  9. [ET93]
    Engelfriet, J., J. Treur: A Temporal Model Theory for Default Logic, in: M. Clarke, R. Kruse, S. Moral (eds), Proc. ECSQARU'93, Lecture Notes in Computer Science, vol. 747, Springer-Verlag, 1993, pp. 91–96Google Scholar
  10. [ET94]
    Engelfriet, J., J. Treur: Temporal Theories of Reasoning. In: C. MacNish, D. Pearce, L.M. Pereira (eds.) Logics in Artificial Intelligence, Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, JELIA'94, Lecture Notes in AI, vol. 838, Springer Verlag, pp. 279–299; Also in: Journal of Applied Non-Classical Logics, vol. 5 (2), 1995, pp. 239–261Google Scholar
  11. [Et87]
    Etherington, D.W.: A semantics for Default Logic, Proc. IJCAI-87, pp. 495–498; see also in: D.W. Etherington, Reasoning with Incomplete Information, Morgan Kaufmann, 1988Google Scholar
  12. [Ga85]
    Gabbay, D.: Theoretical Foundations for Non-monotonic Reasoning in expert systems; in Apt, K. (ed.): Logic and Models of Concurrent Systems, Springer, Berlin, 1985Google Scholar
  13. [Gr88]
    Grove, A.: Two modelings for theory change; Journal of Philosophical Logic 17, 157–170 (1988)CrossRefGoogle Scholar
  14. [He94]
    Herre, H.: Compactness Properties of nonmonotonic Inference Operations, In: C. MacNish, D. Pearce, L.M. Pereira (eds.) Logics in Artificial Intelligence, Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, JELIA'94, Lecture Notes in AI, vol. 838, Springer Verlag, pp. 19–33; Also in: Journal of Applied Non-Classical Logics, vol. 5, 1995, pp. 121–136 (Special Issue with selected papers from JELIA'94)Google Scholar
  15. [Ko88]
    Konolidge, K.: Hierarchic Autoepistemic Theories for Nonmonotonic Reasoning, in: Proceedings AAAI'88, Minneapolis, 1988Google Scholar
  16. [Li91]
    Lindström, S.: A semantic approach to nonmonotonic reasoning: inference operations and choice; Dept. of Philosophy, Uppsala University, Preprint, 1991Google Scholar
  17. [Ma94]
    Makinson, D.: General Patterns in Nonmonotonic Reasoning; in: D.M. Gabbay, C.J. Hogger, J.A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, Vol.3, Oxford Science Publications, 1994Google Scholar
  18. [MT93]
    Marek, V., M. Truszczynski: Nonmonotonic Logic, Springer-Verlag, 1993Google Scholar
  19. [MTT94]
    Marek, V., J. Treur, M. Truszczynski: Representation Theory for Default Logic, Proc. Symposium on AI and Mathematics, 1996Google Scholar
  20. [Po88]
    Poole, D.: A logical Framework for Default Reasoning;Artificial Intelligence, 36: 27–47 (1988)CrossRefMathSciNetGoogle Scholar
  21. [Pop77]
    Popper, K.: The Logic of Scientific Discovery; Hutchinson, London, 1977, 9th edition.Google Scholar
  22. [Re80]
    Reiter, R.: A logic for default reasoning; A.I., vol. 13, 81–132, 1980Google Scholar
  23. [Sh88]
    Shoham, Y.: Reasoning about Change; MIT-Press, Cambridge/USA, 1988Google Scholar
  24. [Ta56]
    Tarski, A.: Logic, Semantics, Metamathematics. Papers from 1923–1938. Clarendon Press, Oxford, 1956Google Scholar
  25. [TT92]
    Tan, Y.H., J. Treur: Constructive Default Logic and the Control of Defeasible Reasoning; in: B. Neumann (ed.), Proc. ECAI'92, Wiley and Sons, 1992, pp. 299–303Google Scholar
  26. [Vo93]
    Voorbraak, F.: Preference-based semantics for nonmonotonic logics,in: Bajcsy, R.(ed), Proc. IJCAI-93, Morgan Kaufmann, 1993, pp. 584–589Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Joeri Engelfriet
    • 1
  • Heinrich Herre
    • 2
  • Jan Treur
    • 1
  1. 1.Department of Mathematics and Computer ScienceFree University AmsterdamHV AmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity of LeipzigLeipzigGermany

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