Skip to main content
Log in

Conditional Ranking Revision

Iterated Revision with Sets of Conditionals

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

In the context of a general framework for belief dynamics which interprets revision as doxastic constraint satisfaction, we discuss a proposal for revising quasi-probabilistic belief measures with finite sets of graded conditionals. The belief states are ranking measures with divisible values (generalizing Spohn’s epistemology), and the conditionals are interpreted as ranking constraints. The approach is inspired by the minimal information paradigm and based on the principle-guided canonical construction of a ranking model of the input conditionals. This is achieved by extending techniques known from conditional default reasoning. We give an overview of how it handles different principles for conditional and parallel revision and compare it with similar accounts.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alchourron, C. E., Gaerdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2), 510–530.

    Article  Google Scholar 

  2. Benferhat, S., Saffiotti, A., & Smets, P. (2000). Belief functions and default reasoning. Artificial Intelligence, 122(1–2), 1–69.

    Article  Google Scholar 

  3. Booth, R., & Meyer, T. (2006). Admissible and restrained revision. Journal of Artificial Intelligence Research, 26, 127–151.

    Google Scholar 

  4. Booth, R., & Meyer, T. (2007). On the dynamics of total preorders: Revising abstract interval orders. In ECSQARU ’07, LNCS 4724 (pp. 42–53). Springer.

  5. Booth, R., Meyer, T. A., & Wong, K. (2006). A bad day surfing is better than a good day working: How to revise a total preorder. In KR ’06 (pp. 230–238). AAAI Press.

  6. Bourne, R. A., & Parsons, S. (2003). Extending the maximum entropy approach to variable-strength defaults. Annals of Mathematics and Artificial Intelligence, 39(1–2), 123–146.

    Article  Google Scholar 

  7. Boutilier, C. (1993). Revision sequences and nested conditionals. In IJCAI ’93 (pp. 519–525). Morgan Kaufmann.

  8. Boutilier, C. (1996). Iterated revision and minimal revision of conditional beliefs. Journal of Philosophical Logic, 25, 262–304.

    Article  Google Scholar 

  9. Boutilier, C., & Goldszmidt, M. (1993). Revision by conditional beliefs. In AAAI ’93 (pp. 649–654). MIT Press.

  10. Chopra, S., Ghose, A., & Meyer, T. (2003). Non-prioritized ranked belief change. Journal of Philosophical Logic, 32(4), 417–443.

    Article  Google Scholar 

  11. Darwiche, A., & Pearl, J. (1997). On the logic of iterated belief revision. Artificial Intelligence, 89(1–2), 1–29.

    Article  Google Scholar 

  12. Delgrande, J. P., & Jin, Y. (2008). Parallel belief revision. In AAAI ’08 (pp. 430–435). AAAI Press.

  13. Delgrande, J., Dubois, D., & Lang, J. (2006). Iterated revision as prioritized merging. In KR ’06 (pp. 210–220). AAAI Press.

  14. Diaye, M.-A., & Schoch, D. (2009). Preference as fulfillment of desires. Journal of Mathematical Psychology, 53(2), 76–85.

    Article  Google Scholar 

  15. Dubois, D., & Prade, H. (1998). Possibility theory: Qualitative and quantitative aspects. In P. Smets (Eds.), Quantified representation of uncertainty and imprecision, Handbook on defeasible reasoning and uncertainty management systems (Vol. 1, pp. 169–226). Dordrecht: Kluwer.

    Google Scholar 

  16. Friedman, N., & Halpern, J. (2001). Plausibility measures and default reasoning. Journal of the ACM, 48(4), 648–685.

    Article  Google Scholar 

  17. Goldszmidt, M., Morris, P., & Pearl, J. (1993). A maximum entropy approach to nonmonotonic reasoning. IEEE Transactions of Pattern Analysis and Machine Intelligence, 15, 220–232.

    Article  Google Scholar 

  18. Hansson, S. O. (1991). Belief contraction without recovery. Studia Logica, 50(2), 251–260.

    Article  Google Scholar 

  19. Hild, M., & Spohn, W. (2008). Measurement of ranks and the laws of iterated contraction. Artificial Intelligence, 172(10), 1195–1218.

    Article  Google Scholar 

  20. Huber, F. (2006). Ranking functions and rankings on languages. Artificial Intelligence, 170(4–5), 462–471.

    Article  Google Scholar 

  21. Jin, Y., & Thielscher, M. (2007). Iterated belief revision, revised. Artificial Intelligence, 171(1), 1–18.

    Article  Google Scholar 

  22. Kern-Isberner, G. (1999). Postulates for conditional belief revision. In IJCAI ’99 (pp. 186–191). Morgan Kaufmann.

  23. Kern-Isberner, G. (2002). Handling conditionals adequately in uncertain reasoning and belief revision. Journal of Applied Non-Classical Logics, 12(2), 215–237.

    Article  Google Scholar 

  24. Kern-Isberner, G. (2004). A thorough axiomatization of a principle of conditional preservation in belief revision. Annals of Mathematics and Artificial Intelligence, 40(1–2), 127–164.

    Article  Google Scholar 

  25. Kern-Isberner, G. (2008). Linking iterated belief change operations to nonmonotonic reasoning. In KR ’08 (pp. 166–176). AAAI Press.

  26. Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models, and cumulative logics. Artificial Intelligence, 44(1–2), 167–207.

    Article  Google Scholar 

  27. Lang, J., van der Torre, L., & Weydert, E. (2002). Utilitarian desires. Autonomous Agents and Multi-Agent Systems, 5(3), 329–363.

    Article  Google Scholar 

  28. Lehmann, D. J. (1995). Belief revision, revised. In IJCAI ’95 (pp. 1534–1540). Morgan Kaufmann.

  29. Nayak, A. C. (1994). Iterated belief change based on epistemic entrenchment. Erkenntnis, 41, 353–390.

    Article  Google Scholar 

  30. Nayak, A. C., Pagnucco, M., & Peppas, P. (2003). Dynamic belief revision operators. Artificial Intelligence, 146(2), 193–228.

    Article  Google Scholar 

  31. Paris, J. (1994). The uncertain reasoner’s companion. Cambridge: Cambridge University Press.

    Google Scholar 

  32. Pearl, J. (1990). System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning. In TARK 3 (pp. 121–135). Morgan Kaufmann.

  33. Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. Oxford Logic Guides (Vol. 42). Oxford: Oxford University Press.

    Google Scholar 

  34. Rott, H. (2009). Shifting priorities: Simple representations for twenty-seven iterated theory change operators. In D. Makinson, J. Malinowski, & H. Wansing (Eds.), Towards mathematical philosophy (pp. 269–296). New York: Springer.

    Chapter  Google Scholar 

  35. Shore, J. E., & Johnson, R. W. (1980). Axiomatic derivation of the principle of cross-entropy minimization. IEEE Transactions on Information Theory, IT-26(1), 26–37.

    Article  Google Scholar 

  36. Spohn, W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states. In W. L. Harper & B. Skyrms (Eds.), Causation in decision, belief change, and statistics (pp. 105–134). Dordrecht: Kluwer.

    Google Scholar 

  37. Spohn, W. (1990). A general non-probabilistic theory of inductive reasoning. In R. D. Shachter, et al. (Eds.), Uncertainty in artificial intelligence (Vol. 4, pp. 149–158). North-Holland, Amsterdam.

  38. Spohn, W. (2009). A survey of ranking theory. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief. An anthology (pp. 185–228). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  39. Weydert, E. (1994). General belief measures. In UAI ’94 (pp. 575–582). Morgan Kaufmann.

  40. Weydert, E. (1995). Default entailment: A preferential construction semantics for defeasible inference. In KI ’95, LNCS 981 (pp. 173–184). Springer.

  41. Weydert, E. (1995). Defaults and infinitesimals. Defeasible inference by non-archimedean entropy maximization. In UAI ’95 (pp. 540–547). Morgan Kaufmann.

  42. Weydert, E. (1996). System J – Revision entailment. In FAPR ’96, LNCS 1085 (pp. 637–649). Springer.

  43. Weydert, E. (1998). System JZ — How to build a canonical ranking model of a default knowledge base. In KR ’98 (pp. 190–201). Morgan Kaufmann.

  44. Weydert, E. (1999). JZBR — Iterated belief change for conditional ranking constraints. Spinning ideas: Electronic essays dedicated to Peter Gaerdenfors on his 50th birthday. http://www.lucs.lu.se/spinning/categories/dynamics/Weydert/index.html.

  45. Weydert, E. (2003). System JLZ — Rational default reasoning by minimal ranking constructions. Journal of Applied Logic (Elsevier), 1(3–4), 273–308.

    Article  Google Scholar 

  46. Weydert, E. (2005). Projective default epistemology — a first look. In Conditionals, information, and inference (Postproceedings of WCII 2002, Hagen, Germany), LNCS 3301 (pp. 65–85). New York: Springer.

    Google Scholar 

  47. Williams, M.-A. (1995). Iterated theory-based change. In IJCAI ’95 (pp. 1541–1550). Morgan Kaufmann.

  48. Zhang, D. (2004). Properties of iterated multiple belief revision. In LPNMR ’04, LNCS 2923 (pp. 314–325). Springer.

  49. Zhang, D., & Foo, N. (2001). Infinitary belief revision. Journal of Philosophical Logic, 30(6), 525–570.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Emil Weydert.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weydert, E. Conditional Ranking Revision. J Philos Logic 41, 237–271 (2012). https://doi.org/10.1007/s10992-011-9204-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-011-9204-4

Keywords

Navigation