Skip to main content
SpringerLink
Log in

Revision of Belief Sets and Belief Bases

  • Chapter
  • First Online:
Belief Change

Part of the book series: Handbook of Defeasible Reasoning and Uncertainty Management Systems ((HAND,volume 3))

Abstract

There are different ways to construct formal models of change. In what may be called time-indexed models, a (discrete or continuous) variable is employed to represent time. The object of change (such as a state of affairs, state of the world, or belief state) can then be represented as a function of this time variable. This framework can also be made indeterministic by allowing for a bundle of functions, typically structured as a branching tree.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. E. Alchourrón, P. Gärdenfors and D. Makinson. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions, Journal of Symbolic Logic, 50, 510–530, 1985.

    MathSciNet  MATH  Google Scholar 

  2. C. E. Alchourrón and D. Makinson. Hierarchies of Regulation and Their Logic, In New Studies in Deontic Logic, Hilpinen, ed. pp. 125–148. D. Reidel Publishing Company, 1981.

    Google Scholar 

  3. C. E. Alchourrón and D. Makinson. On the logic of theory change: Contraction functions and their associated revision functions, Theoria, 48, 14–37, 1982.

    MathSciNet  MATH  Google Scholar 

  4. C. E. Alchourrón and D. Makinson. On the Logic of Theory Change: Safe Contraction, Studia Logica, 44, 405–422, 1985.

    MathSciNet  MATH  Google Scholar 

  5. C. E. Alchourrón and D. Makinson. Maps Between Some Different Kinds of Contraction Function: The Finite Case, Studia Logica, 45, 187–198, 1986.

    MathSciNet  MATH  Google Scholar 

  6. R. J. Brachman and H. J. Levesque. What Makes a Knowledge Base Knowledgeable? A View of Databases from the Knowledge Level, pp. 69–78. In Kerschberg, ed. Expert Database Systems, Proceeding from the first international workshop, The Benjamin/Cummings Publishing Company, 1986.

    Google Scholar 

  7. G. Brewka. Belief revision in a framework for default reasoning, In The Logic of Theory Change, Fuhrmann, ed. pp. 206–222. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  8. J. Collins. Belief, Desire, and Revision, Mind, 97, 333–342, 1988.

    MathSciNet  Google Scholar 

  9. C. B. Cross and R. H. Thomason. Conditionals and knowledge-base update, In Belief Revision, Gärdenfors, ed. pp. 247–275. Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  10. M. Dalai. Investigations Into a Theory of Knowledge Base Revision: Preliminary Report. Seventh National Conference on Artificial Intelligence (AAAI-88). 475–479, 1988.

    Google Scholar 

  11. J. Doyle. A Truth Maintenance System, Artificial Intelligence, 12, 231–272, 1979.

    MathSciNet  Google Scholar 

  12. J. Doyle. Rational belief revision (preliminary report), In Principles of Knowledge Representation and Reasoning, Allen (ed.), pp. 163–174 Morgan Kaufmann, Los Altos, CA, 1991.

    Google Scholar 

  13. J. Doyle. Reason maintenance and belief revision: Foundations versus coherence theories, In Belief Revision, Gärdenfors, ed. pp. 29–51. Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  14. D. Dubois, S. Moral and H. Prade, Belief change rules in ordinal and numerical uncertainty theories, this volume.

    Google Scholar 

  15. D. Dubois and H. Prade. Epistemic entrenchment and possibilistic logic, Artificial Intelligence, 50, 223–239, 1991.

    MathSciNet  MATH  Google Scholar 

  16. A. Fuhrmann. Relevant Logics, Modal Logics, and Theory Change, PhD thesis, Australian National University, Canberra, 1988.

    Google Scholar 

  17. A. Fuhrmann. Theory Contraction Through Base Contraction, Journal of Philosophical Logic, 20, 175–203, 1991.

    MathSciNet  MATH  Google Scholar 

  18. A. Fuhrmann and S. O. Hansson. A Survey of Multiple Contraction, Journal of Logic, Language and Information, 3, 39–75, 1994.

    MathSciNet  MATH  Google Scholar 

  19. J. R. Gallier. Autonomous belief revision and communication, In Belief Revision, Gärdenfors, ed. pp. 220–246. Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  20. A. Grove. Two Modellings for Theory Change, Journal of Philosophical Logic, 17, 157–180, 1988.

    MathSciNet  MATH  Google Scholar 

  21. P. Gärdenfors. Conditionals and Changes of Belief, Acta Philosophica Fennica, 30, 381–404, 1978.

    MATH  Google Scholar 

  22. P. Gärdenfors. An Epistemic Approach to Conditionals, American Philosophical Quarterly, 18, 203–211, 1981.

    Google Scholar 

  23. P. Gärdenfors. Rules for Rational Changes of Belief, Philosophical essays dedicated to L Aqvist, pp. 88–101, 1982.

    Google Scholar 

  24. P. Gärdenfors. Belief Revision and the Ramsey Test for Conditionals, Philosophical Review, 95, 81–93, 1986.

    Google Scholar 

  25. P. Gärdenfors. Knowledge in Flux. Modeling the Dynamics of Epistemic States, The MIT Press, Cambridge, Massachusetts, 1988.

    MATH  Google Scholar 

  26. P. Gärdenfors. The Dynamics of Belief Systems: Foundations vs. Coherence Theories, Revue Internationale de Philosophie, 44, 24–46, 1990.

    Google Scholar 

  27. P. Gärdenfors and D. Makinson. Revisions of Knowledge Systems Using Epistemic Entrenchment. Second Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 83–95, 1988.

    Google Scholar 

  28. P. Gärdenfors and H. Rott. Belief Revision, In Handbook of Logic in AI and Logic Programming, Gabbay, Hogger and Robinson, eds. pp. 35–132. Oxford University Press, Oxford, 1995.

    Google Scholar 

  29. S. O. Hansson. New Operators for Theory Change, Theoria, 55, 114–132, 1989.

    MathSciNet  MATH  Google Scholar 

  30. S. O. Hansson. Belief Base Dynamics, Ph.D. thesis, Uppsala University, 1991.

    Google Scholar 

  31. S. O. Hansson. Belief Contraction Without Recovery, Studia Logica, 50, 251–260, 1991.

    MathSciNet  MATH  Google Scholar 

  32. S. O. Hansson. A Dyadic Representation of Belief, In Belief Revision, Gärdenfors, ed. pp. 89–121. Cambridge University Press, ambridge, 1992.

    Google Scholar 

  33. S. O. Hansson. In Defense of the Ramsey Test, Journal of Philosophy, 89, 522–540, 1992.

    MathSciNet  Google Scholar 

  34. S. O. Hansson. Similarity Semantics and Minimal Changes of Belief, Erkenntnis, 37, 401–429, 1992.

    MathSciNet  Google Scholar 

  35. S. O. Hansson. Changes on Disjunctively Closed Bases, Journal of Logic, Language and Information, 2, 255–284, 1993.

    MathSciNet  MATH  Google Scholar 

  36. S. O. Hansson. Reversing the Levi Identity, Journal of Philosophical Logic, 22, 637–669, 1993.

    MathSciNet  MATH  Google Scholar 

  37. S. O. Hansson. Theory Contraction and Base Contraction Unified, Journal of Symbolic Logic, 58, 602–625, 1993.

    MathSciNet  MATH  Google Scholar 

  38. S. O. Hansson. Kernel Contraction, Journal of Symbolic Logic, 59, 845–859, 1994.

    MathSciNet  MATH  Google Scholar 

  39. S. O. Hansson. Taking Belief Bases Seriously, In Logic and Philosophy of Science in Uppsala, Prawitz, ed. pp. 13–28. Kluwer Academic Publishers, Uppsala, 1994.

    Google Scholar 

  40. S. O. Hansson. Changes in Preference, Theory and Decision, 38, 1–28, 1995.

    MathSciNet  MATH  Google Scholar 

  41. S. O. Hansson. The Emperor’s New Clothes. Some recurring problems in the formal analysis of counterfactuals, In Conditionals: from Philosophy to Computer Science, Crocco, Farinas del Cerro and Herzig, eds. pp. 13–31. Clarendon Press, Oxford, 1995.

    Google Scholar 

  42. S. O. Hansson. Some Solved and Unsolved Remainder Equations, Mathematical Logic Quarterly, 41, 362–368, 1995.

    MathSciNet  MATH  Google Scholar 

  43. S. O. Hansson. A test battery for rational database updating, Artificial Intelligence, 82, 341–352, 1996.

    MathSciNet  Google Scholar 

  44. S. O. Hansson. Recovery and epistemic residue, manuscript, 1997.

    Google Scholar 

  45. S. O. Hansson. Semi-Revision, Journal of Applied Non-Classical Logic, 7, 151–175, 1997.

    MathSciNet  MATH  Google Scholar 

  46. S. O. Hansson. A Textbook of Belief Dynamic, Kluwer, in press, 1997.

    Google Scholar 

  47. S. O. Hansson and D. Makinson. Applying normative rules with restraint, In Logic and Scientific Methods, Dalla Chiara et al., eds. pp. 313–332. Kluwer, 1997.

    Google Scholar 

  48. S. O. Hansson and E. Olsson. Levi contractions and AGM contractions: A comparison, Notre Dame Journal of Formal Logic, 36, 103–119, 1995.

    MathSciNet  MATH  Google Scholar 

  49. S. O. Hansson and E. Olsson. Providing foundations for coherentism, manuscript, 1997.

    Google Scholar 

  50. G. Harman. Change in View. Principles of Reasoning, MIT Press, Cambridge, Mass., 1986.

    Google Scholar 

  51. I. Levi. Subjunctives, Dispositions and Chances, Synthese, 34, 423–455, 1977.

    MATH  Google Scholar 

  52. I. Levi. The Enterprise of Knowledge, The MIT Press,. Cambridge, Massachusetts, 1980.

    Google Scholar 

  53. I. Levi. Iteration of Conditionals and the Ramsey Test, Synthese, 76, 49–81, 1988.

    MathSciNet  Google Scholar 

  54. I. Levi. The Fixation of Belief and Its Undoing, Cambridge University Press, Cambridge, Mass, 1991.

    Google Scholar 

  55. S. Lindström and W. Rabinowicz. On probabilistic representation of non-probabilistic belief revision, Journal of Philosophical Logic, 18, 69–101, 1989.

    MathSciNet  MATH  Google Scholar 

  56. S. Lindström and W. Rabinowicz. Epistemic entrenchment with incomparabilities and relational belief revision, in The Logic of Theory Change, Fuhrmann, ed. pp. 93–126. Springer-Verlag, Berlin, 1991.

    Google Scholar 

  57. S. Lindström, S. and W. Rabinowicz, The Ramsey test revisited. In Conditionals: from Philosophy to Computer Science, G. Crocco, L. Farinas del Cerro and A. Herzig, eds. pp. 147–192. Oxford University Press, 1995.

    Google Scholar 

  58. D. Makinson. On the Status of the Postulate of Recovery in the Logic of Theory Change, Journal of Philosophical Logic, 16, 383–394, 1987.

    MathSciNet  MATH  Google Scholar 

  59. D. Makinson. On the force of some apparent counterexamples to recovery, in Normative Systems in Legal and Moral Theory, Valdés et al., eds. pp. 475–481. Duncker and Humblot, Berlin, 1997.

    Google Scholar 

  60. A. Nayak. Iterated Belief Change Based on Epistemic Entrenchment, Erkenntnis, 41, 353–390, 1994.

    MathSciNet  Google Scholar 

  61. A. Nayak. Foundational Belief Change, Journal of Philosophical Logic, 23, 495–533, 1994.

    MathSciNet  MATH  Google Scholar 

  62. A. Nayak, P. Nelson and H. Polansky. Belief Change as Change in Epistemic Entrenchment, Synthese, 109, 143–174, 1996.

    MathSciNet  MATH  Google Scholar 

  63. B. Nebel. A Knowledge Level Analysis of Belief Revision. 1st International Conference of Principles of Knowledge Representation, pp. 301–311, 1989.

    Google Scholar 

  64. A. Newell. The Knowledge Level, Artificial Intelligence, 18, 87–127, 1982.

    MathSciNet  Google Scholar 

  65. R. Niederée. Multiple contraction. A further case against Gärdenfors’ principleof recovery. In The Logic of Theory Change, Fuhrmann, ed. pp. 322–334. Springer-Verlag, Berlin, 1991.

    MATH  Google Scholar 

  66. W. V. O. Quine. Philosophy of Logic, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1970.

    Google Scholar 

  67. W. V. O. Quine and J. S. Ullian. The Web of Belief, 1978.

    Google Scholar 

  68. H. Rott. Two Methods of Constructing Contractions and Revisions of Knowledge Systems, Journal of Philosophical Logic, 20, 149–173, 1991.

    MathSciNet  MATH  Google Scholar 

  69. H. Rott. On the Logic of Theory Change: More Maps Between Different Kinds of Contraction function. In Belief Revision, Gärdenfors, ed. pp. 122–141. Cambridge University Press, Cambridge, 1992.

    Google Scholar 

  70. H. Rott. Preferential Belief Change Using Generalized Epistemic Entrenchment, Journal of Logic, Language and Information, 1, 45–78, 1992.

    MathSciNet  MATH  Google Scholar 

  71. H. Rott. Belief contraction in the context of the general theory of rational choice, Journal of Symbolic Logic, 58, 1426–1450, 1993.

    MathSciNet  MATH  Google Scholar 

  72. H. Rott. Making Up One’s Mind: Foundations, Coherence, Nonmonotonicity, Book manuscript, 1997.

    Google Scholar 

  73. T. Sandqvist. Why should the best always meet?. In Logic for a Change. Essays dedicated to Sten Lindström on the occasion of his fiftieth birthday, Hansson and Rabinowicz, eds. pp. 125–135. Department of Philosophy, Uppsala University, Uppsala, 1995.

    Google Scholar 

  74. P. Smets. Numerical representations of uncertainty, this volume.

    Google Scholar 

  75. E. Sosa. The Raft and the Pyramid: Coherence versus Foundations in the Theory of Knowledge, Midwest Studies in Philosophy, 5, 3–25, 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Uppsala University, Sweden

    Sven Ove Hansson

Authors
  1. Sven Ove Hansson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Paul Sabatier, Toulouse, France

    Didier Dubois  & Henri Prade  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Hansson, S.O. (1998). Revision of Belief Sets and Belief Bases. In: Dubois, D., Prade, H. (eds) Belief Change. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5054-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5054-5_2

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6123-0

  • Online ISBN: 978-94-011-5054-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation