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Journal of Computer Science and Technology

, Volume 11, Issue 2, pp 108–125 | Cite as

Belief revision by sets of sentences

  • Zhang Dongmo Email author
Article

Abstract

The aim of this paper is to extend the system of belief revision developed by Alchourrón, Gärdenfors and Makinson (AGM) to a more general framework. This extension enables a treatment of revision not only by single sentences but also by any sets of sentences, especially by infinite sets. The extended revision and contraction operators will be called general ones, respectively. A group of postulates for each operator is provided in such a way that it coincides with AGM's in the limit case. A notion of the nice-ordering partition is introduced to characterize the general contraction operation. A computation-oriented approach is provided for belief revision operations.

Keywords

Belief revision the logic of theory change epistemic entrenchment default logic 

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References

  1. [1]
    Alchourrón C E, Gärdenfors P, Makinson D. On the logic of theory change: Partial meet contraction and revision functions.The Journal of Symbolic Logic, 1985, 50(2): 510–530.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Brewka G. Preferred subtheories: An extended logical framework for default reasoning. InProceedings of IJCAI-89, Detroit, Mich. 1989, pp.1034–1048.Google Scholar
  3. [3]
    Brewka G. Cumulative default logic: In defense of nonmonotonic inference rules.Artificial Intelligence, 1991, 50: 183–205.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Boutilier C. Revision sequences and nested conditionals. InProceedings of IJCAI-95, pp.519–525, 1993.Google Scholar
  5. [5]
    Boutilier C. Unifying default reasoning and belief revision in a modal framework.Artificial Intelligence, 1994, 68: 33–85.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Cerro L F, Herzig A, Lang J. From ordering-based nonmonotonic reasoning to conditional logic.Artificial Intelligence, 1994, 66: 375–393.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Dubois D, Prade H. Epistemic entrenchment and possibilistic logic.Artificial Intelligence, 1991, 50: 223–239.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Fuhrmann A. On the modal logic of theory change. InThe Logic of Theory Change (Lecture Notes in Computer Science 465), Fuhrmann A, Morreau M (eds.), Springer-Verlag, 1991, pp.259–281.Google Scholar
  9. [9]
    Fuhrmann A, Hansson S O. A survey of multiple contractions.Journal of Logic, Language, and Information, 1994, 3: 39–76.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Gärdenfors P. Propositional logic based on the dynamics of belief.The Journal of Symbolic Logic 1985, 50(2): 390–394.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Gärdenfors P. Knowledge in Flux: Modeling the Dynamics of Epistemic States. The MIT Press, 1988.Google Scholar
  12. [12]
    Gärdenfors P, Makinson D. Nonmonotonic inference based on expectations.Artificial Intelligence, 1994, 65: 197–245.zbMATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Hansson S O. A dyadic representation of belief. InBelief Revision Gärdenfors P (ed.), Cambridge University Press, Cambridge, 1992, pp.89–121.Google Scholar
  14. [14]
    Hansson S O. Theory contraction and base contraction unified.The Journal of Symbolic Logic, 1993, 58(2): 602–625.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    Hansson S O. Reversing the Levi identityJournal of Philosophical Logic 1993, 22: 637–669.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    Hájek P. Epistemic entrenchment and arithmetical hierarchy.Artificial Intelligence, 1991, 62: 79–87.CrossRefGoogle Scholar
  17. [17]
    Jech T. Set Theory. Academic Press, New York, 1978.Google Scholar
  18. [18]
    Katsuno H, Mendelzon A O. Propositional knowledge base revision and minimal change.Artificial Intelligence, 1991, 52: 203–294.CrossRefMathSciNetGoogle Scholar
  19. [19]
    Makinson D, Gärdenfors P. Relations between the logic of theory change and nonmonotonic logic. InThe Logic of Theory Change, (Lecture Notes in Computer Science 465), Fuhrmann A, Morreau M (eds.), Springer-Verlag, Berlin, Germany, 1991, pp.185–205.Google Scholar
  20. [20]
    Nebel B. Reasoning and Revision in Hybrid Representation System (Lecture Notes in Artificial Intelligence 422). Springer-Verlag, 1990.Google Scholar
  21. [21]
    Nebel B. Syntax based approaches to belief revision. InBelief Revision, Gärdenfors P (ed.), Cambridge University Press, Cambridge, 1992, 52–88.Google Scholar
  22. [22]
    Niederèe R. Multiple contraction: A further case against Gärdenfors' principle of recovery. InThe Logic of Theory Change (Lecture Notes in Computer Science 465), Fuhrmann A, Morreau M (eds.), Springer-Verlag, 1991, pp.322–334.Google Scholar
  23. [23]
    Rott H. On the logic of theory change: More maps between different kinds of contraction function. InBelief Revision, Gärdenfors P (ed.), Cambridge University Press, Cambridge, 1992, pp. 122–140.Google Scholar
  24. [24]
    Rott H. Belief contraction in the context of the general theory of rational choice.The Journal of Symbolic Logic, 1993, 58(4): 1426–1450.zbMATHCrossRefMathSciNetGoogle Scholar
  25. [25]
    Weydert E. Relevance and revision: About generalizing syntax-based belief revision. InEuropean Workshop JELIA'92 (Lecture Notes in Artificial Intelligence 633), Pearce D, Wagner G (eds.), Springer-Verlag, Berlin, 1992, pp. 126–138.Google Scholar
  26. [26]
    Zhang Dongmo. A general framework for belief revision. InProc. of 4th Int'l Conf. for Young Computer Scientists, Peking University Press, 1995, 574–581.Google Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 1996

Authors and Affiliations

  1. 1.Department of Computer ScienceNanjing University of Aeronautics and AstronauticsNanjing

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