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Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators

  • Hans RottEmail author
Chapter
Part of the Trends in Logic book series (TREN, volume 28)

Abstract

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers.

Keywords

theory change belief bases belief revision prioritization iteration two-dimensional revision operators 

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References

  1. [Alchourrón, Gärdenfors and Makinson, 1985]
    Alchourrón, Carlos, Gärdenfors, Peter, Makinson, David (1985), ‘On the logic of theory change: Partial meet contraction functions and their associated revision functions’, Journal of Symbolic Logic, 50: 510–530, zbMATHCrossRefMathSciNetGoogle Scholar
  2. [Areces and Becher, 2001]
    Areces, Carlos, Becher, Veronica (2001), ‘Iterable AGM functions’, in Williams, Rott (eds.), pp. 261–277. Google Scholar
  3. [Benferhat, Dubois and Prade, 2001]
    Benferhat, Salem, Dubois, Didier, Prade, Henri (2001), ‘A computational model for belief change and fusing ordered belief bases’, in Williams, Rott (eds.), pp. 109–134. Google Scholar
  4. [Booth and Meyer, 2006]
    Booth, Richard, Meyer, Thomas (2006), ‘Admissible and restrained revision’, Journal of Artificial Intelligence Research, 26: 127–151. MathSciNetzbMATHGoogle Scholar
  5. [Boutilier, 1993]
    Boutilier, Craig, (1993), ‘Revision sequences and nested conditionals’, in Bajcsy, R. (ed.), IJCAI-93—Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pp. 519–525. Google Scholar
  6. [Boutilier, 1996]
    Boutilier, Craig (1996), ‘Iterated revision and minimal change of conditional beliefs’, Journal of Philosophical Logic, 25: 263–305. zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Cantwell, 1997]
    Cantwell, John (1997), ‘On the logic of small changes in hypertheories’, Theoria, 63: 54–89. MathSciNetCrossRefGoogle Scholar
  8. [Darwiche and Pearl, 1997]
    Darwiche, Adnan, Pearl, Judea (1997), ‘On the logic of iterated belief revision’, Artificial intelligence, 89: 1–29. zbMATHCrossRefMathSciNetGoogle Scholar
  9. [Dubois, Lang and Prade, 1994]
    Dubois, Didier, Lang, Jérôme, Prade, Henri, ‘Possibilistic logic’, in: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, Nonmonotonic Reasoning and Uncertain Reasoning, Clarendon Press, Oxford, 1994, pp. 439–513. Google Scholar
  10. [Fermé, 2000]
    Fermé, Eduardo (2000), ‘Irrevocable belief revision and epistemic entrenchment’, Logic Journal of the IGPL, 8: 645–652. zbMATHCrossRefGoogle Scholar
  11. [Fermé and Rodriguez, 1998]
    Fermé, Eduardo, Rodriguez, Ricardo (1998), ‘A brief note about Rott contraction’, Logic Journal of the IGPL, 6: 835–842. zbMATHCrossRefGoogle Scholar
  12. [Fermé and Rott, 2004]
    Fermé, Eduardo, Rott, Hans (2004), ‘Revision by comparison’, Artificial Intelligence, 157: 5–47. zbMATHCrossRefMathSciNetGoogle Scholar
  13. [Gärdenfors and Makinson, 1988]
    Gärdenfors, Peter, Makinson, David (1988), ‘Revisions of knowledge systems using epistemic entrenchment’, in Vardi, M. (ed.), Theoretical Aspects of Reasoning About Knowledge, Morgan Kaufmann, Los Altos, CA, 1988, pp. 83–95. Google Scholar
  14. [Grove, 1988]
    Grove, Adam (1988), ‘Two modellings for theory change’, Journal of Philosophical Logic, 17: 157–170. zbMATHCrossRefMathSciNetGoogle Scholar
  15. [Hansson, 1999]
    Hansson, Sven O. (1999), A Textbook of Belief Dynamics. Theory Change and Database Updating, Kluwer, Dordrecht. zbMATHGoogle Scholar
  16. [Levi, 2004]
    Levi, Isaac (2004), Mild Contraction: Evaluating Loss of Information due to Loss of Belief, Oxford University Press, Oxford. Google Scholar
  17. [Lewis, 1973]
    Lewis, David (1973), Counterfactuals, Blackwell, Oxford. Google Scholar
  18. [Meyer, Ghose and Chopra, 2001]
    Meyer, Thomas, Ghose, Aditya, Chopra, Samir (2001), ‘Syntactic representations of semantic merging operations’, in Proceedings of the IJCAI-2001 Workshop on Inconsistency in Data and Knowledge, Seattle, USA, August 2001, pp. 36–42. Google Scholar
  19. [Nayak, 1994]
    Nayak, Abhaya C. (1994), ‘Iterated belief change based on epistemic entrenchment’, Erkenntnis, 41: 353–390. CrossRefMathSciNetGoogle Scholar
  20. [Nayak, Pagnucco and Peppas, 2003]
    Nayak, Abhaya C., Pagnucco, Maurice, Peppas, Pavlos (2003), ‘Dynamic belief revision operators’, Artificial Intelligence, 146: 193–228. zbMATHCrossRefMathSciNetGoogle Scholar
  21. [Nayak, Goebel and Orgun, 2007]
    Nayak, Abhaya, Goebel, Randy, Orgun, Mehmet (2007), ‘Iterated belief contraction from first principles’, International Joint Conference on Artificial Intelligence (IJCAI’07), pp. 2568–2573. Google Scholar
  22. [Nebel, 1992]
    Nebel, Bernhard (1992), ‘Syntax-based approaches to belief revision’, in: Gärdenfors, Peter (ed.), Belief Revision, Cambridge University Press, Cambridge, pp. 52–88. Google Scholar
  23. [Pagnucco and Rott, 1999]
    Pagnucco, Maurice, Rott, Hans (1999), ‘Severe withdrawal—and recovery’, Journal of Philosophical Logic, 28: 501–547. (Full corrected reprint in the JPL issue of February 2000.) zbMATHCrossRefMathSciNetGoogle Scholar
  24. [Papini, 2001]
    Papini, Odile (2001), ‘Iterated revision operations stemming from the history of an agent’s observations’, in Williams, Rott (eds.), pp. 279–301. Google Scholar
  25. [Peirce, 1903]
    Peirce, Charles S. (1903), ‘The nature of meaning’, Harvard Lecture delivered on 7 May 1903, published in The Essential Peirce, vol. 2 (1803–1913), ed. by the Peirce Edition Project, Indiana University Press, Bloomington, 1998, pp. 208–225. Google Scholar
  26. [Rescher, 1964]
    Rescher, Nicholas (1964), Hypothetical Reasoning, North-Holland, Amsterdam. Google Scholar
  27. [Rott, 1991a]
    Rott, Hans (1991a), ‘Two methods of constructing contractions and revisions of knowledge systems’, Journal of Philosophical Logic, 20: 149–173. zbMATHCrossRefMathSciNetGoogle Scholar
  28. [Rott, 1991b]
    Rott, Hans (1991b), ‘A non-monotonic conditional logic for belief revision I’, in Fuhrmann, A., Morreau, M., The Logic of Theory Change, LNCS vol. 465, Springer, Berlin, pp. 135–181. CrossRefGoogle Scholar
  29. [Rott, 1992]
    Rott, Hans (1992), ‘Modellings for belief change: Prioritization and entrenchment’, Theoria, 58: 21–57. zbMATHMathSciNetGoogle Scholar
  30. [Rott, 2000]
    Rott, Hans (2000), ‘ “Just because”: Taking belief bases- seriously’, in Buss, Samuel R., Hájek, Petr, Pudlák, Pavel (eds.), Logic Colloquium ’98—Proceedings of the 1998 ASL European Summer Meeting, Lecture Notes in Logic, vol. 13, Urbana, Ill. Association for Symbolic Logic, pp. 387–408. Google Scholar
  31. [Rott, 2001]
    Rott, Hans (2001), Change, Choice and Inference, Oxford University Press, Oxford. zbMATHGoogle Scholar
  32. [Rott, 2003]
    Rott, Hans (2003), ‘Coherence and conservatism in the dynamics of belief. Part II: Iterated belief change without dispositional coherence’, Journal of Logic and Computation, 13: 111–145. zbMATHCrossRefMathSciNetGoogle Scholar
  33. [Rott, 2004]
    Rott, Hans (2004), ‘Stability, strength and sensitivity: converting belief into knowledge’, in Brendel, Elke, Jäger, Christoph (eds.), Contextualisms in Epistemology, special issue of Erkenntnis 61: 469–493. Google Scholar
  34. [Rott, 2006]
    Rott, Hans (2006), ‘Revision by comparison as a unifying framework: Severe withdrawal, irrevocable revision and irrefutable revision’, Theoretical Computer Science, 355: 228–242. zbMATHCrossRefMathSciNetGoogle Scholar
  35. [Rott, 2007]
    Rott, Hans (2007), ‘Bounded revision: Two-dimensional belief change between conservatism and moderation’, in Rønnow-Rasmussen, Toni et al. (eds.), Hommage à Wlodek. Philosophical Papers Dedicated to Wlodek Rabinowicz, internet publication, http://www.fil.lu.se/hommageawlodek/site/abstra.htm. Google Scholar
  36. [Segerberg, 1998]
    Segerberg, Krister (1998), ‘Irrevocable belief revision in dynamic doxastic logic’, Notre Dame Journal of Formal Logic, 39: 287–306. zbMATHCrossRefMathSciNetGoogle Scholar
  37. [Spohn, 1988]
    Spohn, Wolfgang (1988), ‘Ordinal conditional functions’, in Harper, W.L., Skyrms, B. (eds.), Causation in Decision, Belief Change, and Statistics, vol. II, Reidel, Dordrecht, pp. 105–134. Google Scholar
  38. [Stalnaker, 1996]
    Stalnaker, Robert (1996), ‘Knowledge, belief, and counterfactual reasoning in games’, Economics and Philosophy, 12: 133–163. CrossRefGoogle Scholar
  39. [Williams, 1994]
    Williams, Mary-Anne (1994), On the logic of theory base change’, in MacNish, C., Pearce, D., Pereira, L.M. (eds.), Logics in Artificial Intelligence, LNCS, vol. 838, Springer, Berlin, pp. 86–105. CrossRefGoogle Scholar
  40. [Williams, 1995]
    Williams, Mary-Anne (1995), ‘Iterated theory base change: A computational model’, in IJCAI’95—Proceedings of the 14th International Joint Conference on Artificial Intelligence, Morgan Kaufmann, San Mateo, pp. 1541–1550. Google Scholar
  41. [Williams and Rott, 2001]
    Williams, Mary-Anne, Rott, Hans (eds.), (2001), Frontiers in Belief Revision, Kluwer, Dordrecht. Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut für PhilosophieUniversität RegensburgRegensburgGermany

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