Papers
Topics
Authors
Recent
Search
2000 character limit reached

Characterization of AGM Belief Contraction in Terms of Conditionals

Published 11 Jul 2023 in cs.AI and cs.LO | (2307.05629v1)

Abstract: We provide a semantic characterization of AGM belief contraction based on frames consisting of a Kripke belief relation and a Stalnaker-Lewis selection function. The central idea is as follows. Let K be the initial belief set and K-A be the contraction of K by the formula A; then B belongs to the set K-A if and only if, at the actual state, the agent believes B and believes that if not-A is (were) the case then B is (would be) the case.

Authors (1)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (34)
  1. Carlos Alchourrón, Peter Gärdenfors & David Makinson (1985): On the logic of theory change: partial meet contraction and revision functions. The Journal of Symbolic Logic 50, pp. 510–530, 10.2307/2274239.
  2. Giacomo Bonanno (2023): A Kripke-Stalnaker-Lewis semantics for AGM belief revision. Technical Report, REPEC preprint No. 354. Available at https://econpapers.repec.org/paper/cdawpaper/354.htm.
  3. Journal of Philosophical Logic 37(5), pp. 501–520, 10.1007/s10992-008-9086-2.
  4. Eduardo Fermé (1998): On the Logic of Theory Change: Contraction without Recovery. Journal of Logic, Language, and Information 7(2), pp. 127–137, 10.1023/A:1008241816078.
  5. Eduardo Fermé & Sven Ove Hansson (2011): AGM 25 Years. Journal of Philosophical Logic 40, pp. 295–331, 10.1007/S10992-011-9171-9.
  6. Eduardo Fermé & Sven Ove Hansson (2018): Belief change: introduction and overview. Springer, 10.1007/978-3-319-60535-7.
  7. Eduardo Fermé & Ricardo Rodriguez (1998): Semi-Contraction: Axioms and Construction. Notre Dame Journal of Formal Logic 39(3), pp. 332–345, 10.1305/ndjfl/1039182250.
  8. Nir Friedman & Joseph Halpern (1994): Conditional logics of belief change. In Barbara Hayes-Roth & Richard Korf, editors: AAAI’94: Proceedings, AAAI Press, pp. 915–921. Available at https://dl.acm.org/doi/proceedings/10.5555/2891730.
  9. André Fuhrmann (1991): Theory contraction through base contraction. Journal of Philosophical Logic 20, pp. 175–203, 10.1007/BF00284974.
  10. Peter Gärdenfors (1986): Belief Revisions and the Ramsey Test for Conditionals. Philosophical Review 95(1), pp. 81–93, 10.2307/2185133.
  11. Peter Gärdenfors (1988): Knowledge in flux: modeling the dynamics of epistemic states. MIT Press. Available at https://www.collegepublications.co.uk/logic/lcs/?00004.
  12. Konstantinos Georgatos (2017): Epistemic Conditionals and the Logic of Subsets. In Ramaswamy Ramanujam, Lawrence Moss & Can Başkent, editors: Rohit Parikh on Logic, Language and Society, Springer Verlag, pp. 259–277, 10.1007/978-3-319-47843-2.
  13. Adam Grove (1988): Two modellings for theory change. Journal of Philosophical Logic 17, pp. 157–170, 10.1007/BF00247909.
  14. Sven Ove Hansson (1991): Belief contraction without recovery. Studia Logica 50(2), pp. 251–260, 10.1007/BF00370186.
  15. Sven Ove Hansson (1996): Hidden structures of belief. In Andre Fuhrmann & Hans Rott, editors: Logic, Actions and Information, de Gruyter, pp. 79–100. Available at https://www.degruyter.com/document/isbn/9783110868890/html?lang=en.
  16. Sven Ove Hansson (1999): Recovery and epistemic residue. Journal of Logic, Language and Information 8, pp. 421–428, 10.1023/A:1008316915066.
  17. Sven Ove Hansson (1999): A textbook of belief dynamics: Theory change and database updating. Springer Dordrecht, Dordrecht, 10.1007/978-94-007-0814-3.
  18. Sébastien Konieczny & Ramón Pino Pérez (2017): On Iterated Contraction: Syntactic Characterization, Representation Theorem and Limitations of the Levi Identity. In Serafín Moral, Olivier Pivert, Daniel Sánchez & Nicolás Marín, editors: Scalable Uncertainty Management, Springer International Publishing, pp. 348–362, 10.1007/978-3-319-67582-4_25.
  19. Isaac Levi (1991): The fixation of belief and its undoing. Cambridge University Press, 10.1017/CBO9780511663819.
  20. Isaac Levi (2004): Mild Contraction. Oxford University Press, 10.1093/0199270708.001.0001.
  21. David Lewis (1973): Counterfactuals. Harvard University Press. Available at https://www.wiley.com/en-us/Counterfactuals-p-9780631224259.
  22. Sten Lindström & Wlodek Rabinowicz (1991): Epistemic entrenchment with incomparabilities and relational belief revision. In André Fuhrmann & Michael Morreau, editors: The Logic of Theory Change, Springer, pp. 93–126, 10.1007/BFb0018418.
  23. Sten Lindström & Wlodek Rabinowicz (1998): Conditionals and the Ramsey Test. In Didier Dubois & Henri Prade, editors: Belief Change, Springer Netherlands, Dordrecht, pp. 147–188, 10.1007/978-94-011-5054-5_4.
  24. Sten Linström & Wlodzimierz Rabinowicz (1992): The Ramsey test revisited*. Theoria 58(2-3), pp. 131–182, 10.1111/j.1755-2567.1992.tb01138.x.
  25. David Makinson (1987): On the status of the postulate of recovery in the logic of theory change. Journal of Philosophical Logic 16, pp. 383–394, 10.1007/BF00431184.
  26. Journal of Philosophical Logic 31(5), pp. 415–443, 10.1023/A:1020199115746.
  27. Lawrence S Moss & Rohit Parikh (1992): Topological reasoning and the logic of knowledge: preliminary report. In Yoram Moses, editor: Proceedings of the 4th Conference on Theoretical Aspects of Reasoning about Knowledge (TARK 1992), Morgan Kaufmann, pp. 95– 105.
  28. Reinhard Niederée (1991): Multiple contraction a further case against Gärdenfors’ principle of recovery. In André Fuhrmann & Michael Morreau, editors: The Logic of Theory Change, Springer, pp. 322–334, 10.1007/BFb0018427.
  29. Frank P. Ramsey (1950): General Propositions and Causality. In R. B. Braithwaite, editor: The Foundations of Mathematics and other Logical Essays, Humanities Press, pp. 237–257, 10.4324/9781315887814.
  30. Erkenntnis 25(3), pp. 345–370, 10.1007/BF00175348.
  31. Hans Rott (2017): Preservation and postulation: lessons from the new debate on the Ramsey test. Mind 126(502), pp. 609–626, 10.1093/mind/fzw028.
  32. Hans Rott & Maurice Pagnucco (1999): Severe Withdrawal (and Recovery). Journal of Philosophical Logic 28(5), pp. 501–547, 10.1023/A:1004344003217.
  33. Kai Sauerwald, Gabriele Kern-Isberner & Christoph Beierle (2020): A conditional perspective for iterated belief contraction. In G.D. Giacomo et al, editor: ECAI 2020, IOS Press, Berlin, Heidelberg, pp. 889–896. Available at 10.3233/FAIA200180.
  34. Robert Stalnaker (1968): A theory of conditionals. In N. Rescher, editor: Studies in logical theory, Blackwell, pp. 98–112, 10.1007/978-94-009-9117-0_2.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up