Studia Logica

, Volume 86, Issue 2, pp 299–329 | Cite as

The Consistency Argument for Ranking Functions



The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.


Conditionalization Conditional Consistency Consistency Consistency Argu­ment Consistency Theorem Deductive Closure Dutch Book Argument Ranking Func­tions Probability Measures Revision Spohn Update Rule 


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  1. 1.
    Armendt Brad (1980), ‘Is there a Dutch Book Argument for Probability Kinema­tics?’. Philosophy of Science 47, 583–588CrossRefGoogle Scholar
  2. 2.
    Armendt Brad (1993), ‘Dutch Books, Additivity, and Utility Theory’. Philosophi­cal Topics 21,1–20Google Scholar
  3. 3.
    Bronfman Aaron (manuscript), A Gap in Joyce’s Argument for Probabilism.Google Scholar
  4. 4.
    Christensen David (1996), ‘Dutch-Book Arguments Depragmatized: Epistemic Consistency for Partial Believers’. Journal of Philosophy 93,450–479CrossRefGoogle Scholar
  5. 5.
    Dempster Arthur P.(1968), ‘A Generalization of Bayesian Inference’. Journal of the Royal Statistical Society B 30, 205–247Google Scholar
  6. 6.
    Dubois Didier, Henri Prade (1988), Possibility Theory. An Approach to Computerized Processing of Uncertainty, NewYork, Plenum PressGoogle Scholar
  7. 7.
    Eriksson Lina, Alan Hájek (2007), ‘What Are Degrees of Belief?’ Studia Logica 86(2):185–215CrossRefGoogle Scholar
  8. 8.
    Field Hartry (1978), ‘A Note on Jeffrey Conditionalization’. Philosophy of Science 45, 361–367CrossRefGoogle Scholar
  9. 9.
    Fitelson Branden (1999), ‘The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity’. Philosophy of Science 66, S362–S378CrossRefGoogle Scholar
  10. 10.
    Garber Daniel (1980), ‘Field and Jeffrey Conditionalization’. Philosophy of Sci­ence 47, 142–145CrossRefGoogle Scholar
  11. 11.
    Gärdenfors Peter, Hans Rott (1995), ‘Belief Revision’, in D.M. Gabbay, C.J. Hogger, and J.A. Robinson (eds.), Handbook of Logicin Artificial Intelligence and Logic Programming. Vol. 4. Epistemic and Temporal Reasoning, Oxford: Clarendon Press, 35–132.Google Scholar
  12. 12.
    Halpern Joseph Y.(2003), Reasoning About Uncertainty. Cambridge, MA, MIT PressGoogle Scholar
  13. 13.
    Hájek Alan (2005), ‘Scotching Dutch Books?’. Philosophical Perspectives 19, 139– 151CrossRefGoogle Scholar
  14. 14.
    Hájek, Alan (to appear), ‘Arguments for - or against - Probabilism?’, in F. Huber and C. Schmidt-Petri (eds.), Degrees of Belief.Google Scholar
  15. 15.
    Hempel Carl Gustav (1962) ‘Deductive-Nomological vs Statistical Explanation’, In: Feigl H., Maxwell G. (eds). Scientific Explanation, Space and Time. Minnesota Studies in the Philosophy of Science 3. University of Minnesota Press, Minneapolis, 98–169.Google Scholar
  16. 16.
    Hintikka Jaakko (1962) Knowledge and Belief, An Introduction to the Logic of theTwo Notions. Cornell University Press, Ithaca, NYGoogle Scholar
  17. 17.
    Howson, Colin (manuscript), Countable Additivity, Coherence, and Consistency.Google Scholar
  18. 18.
    Howson Colin, Allan Franklin (1994), ‘Bayesian Conditionalization and Probability Kinematics’. British Journal for the Philosophy of Science 45,451–466CrossRefGoogle Scholar
  19. 19.
    Huber Franz (2006), ‘Ranking Functions and Rankings on Languages’. Artificial Intelligence 170, 462–471CrossRefGoogle Scholar
  20. 20.
    Jeffrey Richard C. (1983) The Logic of Decision. 2nd ed. Chicago: University of Chicago PressGoogle Scholar
  21. 21.
    Joyce James M. (1998), ‘A Nonpragmatic Vindication of Probabilism’. Philosophy of Science 65,575–603CrossRefGoogle Scholar
  22. 22.
    Kant, Immanuel (1902), Kants gesammelte Schriften. Ed. by the Königlich Preussische (now Deutsche) Akademie der Wissenschaften. Berlin: G. Reimer (now de Gruyter).Google Scholar
  23. 23.
    Kyburg Henry E. (1961) Probability and the Logic of Rational Belief. Middletown, CT: Wesleyan University PressGoogle Scholar
  24. 24.
    Lewis David (1973) Counterfactuals. Cambridge, MA: Harvard University PressGoogle Scholar
  25. 25.
    Maher Patrick (2002), ‘Joyce’s Argument for Probabilism’. Philosophy of Science 69, 73–81CrossRefGoogle Scholar
  26. 26.
    Milne, Peter (1996), ‘log [P (h | eb) / P (h/b)] is the One True Measure of Confirmation’, Philosophy of Science 63,21–26.Google Scholar
  27. 27.
    Ramsey, Frank P. (1926), ‘Truthand Probability’, in F.P. Ramsey (1931), The Foundations of Mathematics and Other Logical Essays. Ed. by R.B. Braithwaite. London: Kegan, Paul, Trench, Trubner & Co., New York: Harcourt, Brace and Company, 156–198.Google Scholar
  28. 28.
    Rott Hans (2001) Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning. Oxford University Press, OxfordGoogle Scholar
  29. 29.
    Shafer Glenn (1976) A Mathematical Theory of Evidence. Princeton: Princeton University PressGoogle Scholar
  30. 30.
    Shenoy Prakash P.(1991), ‘On Spohn’s Rule for Revision of Beliefs’. International Journal of Approximate Reasoning 5,149–181CrossRefGoogle Scholar
  31. 31.
    Shimony Abner (1955), ‘Coherence and the Axioms of Confirmation’. Journal of Symbolic Logic 20,1–28CrossRefGoogle Scholar
  32. 32.
    Skyrms Brian (1984) Pragmatism and Empiricism. Yale: Yale University PressGoogle Scholar
  33. 33.
    Smullyan Raymond M. (1968) First-Order Logic. Berlin: SpringerGoogle Scholar
  34. 34.
    Spohn, Wolfgang (1988), ‘Ordinal Conditional Functions: A Dynamic Theory of Epistemic States’, in W.L. Harper, and B. Skyrms (eds.), Causationin Decision, Belief Change, and Statistics II, Dordrecht: Kluwer,105–134.Google Scholar
  35. 35.
    Spohn, Wolfgang (1990), ‘A General Non-Probabilistic Theory of Inductive Reasoning’, in R.D. Shachter, T.S. Levitt, and J. Lemmer and L.N. Kanal (eds.), Uncer­tainty in Artificial Intelligence 4. Amsterdam: North-Holland, 149–158.Google Scholar
  36. 36.
    Spohn, Wolfgang (1999), ‘Ranking Functions, AGM Style’, in B. Hansson, S. Halldén, N.-E. Sahlin, and W. Rabinowicz (eds.), Internet Festschrift for Peter Gär­denfors, Lund.Google Scholar
  37. 37.
    Spohn, Wolfgang (to appear), ‘A Survey of Ranking Theory’, in F. Huber and C. Schmidt-Petri (eds.), Degrees of Belief.Google Scholar
  38. 38.
    Spohn, Wolfgang (manuscript), Ranking Theory.Google Scholar
  39. 39.
    Stalnaker, Robert (1968), ‘A Theory of Conditionals’, in N. Rescher (ed.), Studies in Logical Theory. American Philosophical Quaterly Monograph Series 4. Oxford: Blackwell, 98–112.Google Scholar
  40. 40.
    Teller Paul (1973), ‘Conditionalization and Observation’. Synthese 26, 218–258CrossRefGoogle Scholar
  41. 41.
    Zadeh Lotfi A. (1978) ‘Fuzzy Sets as a Basis for a Theory of Possibility’. Fuzzy Sets and Systems 1: 3–28CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Division of Humanities and Social SciencesCalifornia Institute of TechnologyPasadenaUSA

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