, Volume 79, Supplement 6, pp 1219–1252 | Cite as

Two Concepts of Plausibility in Default Reasoning

  • Hans RottEmail author
Original Article


In their unifying theory to model uncertainty, Friedman and Halpern (1995–2003) applied plausibility measures to default reasoning satisfying certain sets of axioms. They proposed a distinctive condition for plausibility measures that characterizes “qualitative” reasoning (as contrasted with probabilistic reasoning). A similar and similarly fundamental, but more general and thus stronger condition was independently suggested in the context of “basic” entrenchment-based belief revision by Rott (1996–2003). The present paper analyzes the relation between the two approaches to formalizing basic notions of plausibility as used in qualitative default reasoning. While neither approach is a special case of the other, translations can be found that elucidate their relationship. I argue that Rott’s notion of plausibility allows for a more modular set-up and has a better philosophical motivation than that of Friedman and Halpern.



I would like to thank David Etlin, Joe Halpern, Hannes Leitgeb, an anonymous referee of Erkenntnis, as well as audiences of two workshops on Halpern’s work (July 2011) and on “Philosophical Issues in Belief Revision, Conditionals and Possible Worlds Semantics” (September 2012) at the University of Konstanz, and of the Ninth Annual Formal Epistemology Workshop in Munich (May/June 2012) for helpful comments on earlier versions of this paper. They have led to substantial improvements.


  1. Adams, E. W. (1975). The logic of conditionals. Dordrecht: Reidel.CrossRefGoogle Scholar
  2. Alchourrón, C. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50, 510–530.CrossRefGoogle Scholar
  3. Alchourrón, C. E., & Makinson, D. (1985). On the logic of theory change: Safe contraction. Studia Logica, 44, 405–422.CrossRefGoogle Scholar
  4. Dubois, D., Fargier, H., & Prade, H. (2004). Ordinal and probabilistic representations of acceptance. Journal of Artificial Intelligence Research, 22, 23–56.Google Scholar
  5. Dubois, D., & Prade, H. (1991). Possibilistic logic, preferential models, non-monotonicity and related issues. In Proceedings twelfth international joint conference on artificial intelligence (IJCAI’91) (pp. 419–424). San Francisco: Morgan Kaufmann.Google Scholar
  6. Dubois, D., & Prade, H. (1995). Numerical representations of acceptance. In Proceedings of the 11th conference on uncertainty in artificial intelligence (UAI’95) (pp. 149–156). San Francisco: Morgan Kaufmann.Google Scholar
  7. Freund, M. (1993). Injective models and disjunctive relations. Journal of Logic and Computation, 3, 231–247.CrossRefGoogle Scholar
  8. Freund, M. (1998). Preferential orders and plausibility measures. Journal of Logic and Computation, 8, 147–158.CrossRefGoogle Scholar
  9. Friedman, N. (1997). Modeling beliefs in dynamic systems, PhD thesis, Stanford University.Google Scholar
  10. Friedman, N., & Halpern, J. Y. (1995). Plausibility measures: A user’s guide. In Proceedings of the 11th conference on uncertainty in artificial intelligence (UAI’95) (pp. 175–184). San Francisco: Morgan Kaufmann.Google Scholar
  11. Friedman, N., & Halpern, J. Y. (1996). Plausibility measures and default reasoning. In Proceedings of the 13th national conference on artificial intelligence (AAAI’96), Portland, OR, pp. 1297–1304.Google Scholar
  12. Friedman, N., & Halpern, J. Y. (1999). Plausibility measures and default reasoning: An overview. In Proceedings of the 14th symposium on logic in computer science (LICS’99), pp. 130–135.Google Scholar
  13. Friedman, N., & Halpern, J. Y. (2001). Plausibility measures and default reasoning. Journal of the ACM, 48, 648–685.CrossRefGoogle Scholar
  14. Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of epistemic states. Cambridge, Mass: Bradford Books, MIT Press.Google Scholar
  15. Gärdenfors, P. (1990). Belief revision and nonmonotonic logic: Two sides of the same coin? In L. C. Aiello (Ed.), 9th European conference on artificial intelligence (ECAI’90) (pp. 768–773). London: Pitman. Google Scholar
  16. Gärdenfors, P., & Makinson, D. (1994). Nonmonotonic inference based on expectations. Artificial Intelligence, 65, 197–245.CrossRefGoogle Scholar
  17. Geffner, H. (1992). High probabilities, model preference and default arguments. Minds and Machines, 2, 51–70.CrossRefGoogle Scholar
  18. Goldszmidt, M., & Pearl, J. (1992). Rank-based systems: A simple approach to belief revision, belief update, and reasoning about evidence and actions. In Proceedings of the third international conference on principles of knowledge representation and reasoning (KR’92) (pp. 661–672). Cambridge, Mass.: Morgan Kaufmann.Google Scholar
  19. Halpern, J. Y. (1997). Defining relative likelihood in partially-ordered preferential structures. Journal of Artificial Intelligence Research, 7, 1–24.Google Scholar
  20. Halpern, J. Y. (2001). Plausibility measures: A general approach for representing uncertainty. In Proceedings of the 17th joint conference on artificial intelligence (IJCAI’2001) (pp. 1474–1483). San Francisco: Morgan Kaufmann.Google Scholar
  21. Halpern, J. Y. (2003). Reasoning about uncertainty. Cambridge, Mass.: MIT Press.Google Scholar
  22. Hawthorne, J. (1996). On the logic of nonmonotonic conditionals and conditional probabilities. Journal of Philosophical Logic, 25, 185–218.Google Scholar
  23. James, W. (1975). Pragmatism—a new name for some old ways of thinking (1907), vol. 1 of the works of William James. Cambridge, Mass., and London: Harvard University Press.Google Scholar
  24. Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.CrossRefGoogle Scholar
  25. Lehmann, D., & Magidor, M. (1992). What does a conditional knowledge base entail? Artificial Intelligence, 55, 1–60.CrossRefGoogle Scholar
  26. Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.Google Scholar
  27. Pearl, J. (1990). System Z: A natural ordering of defaults with tractable applications to default reasoning. In R. Parikh (Ed.), Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge (pp. 121–135). San Mateo: Morgan Kaufmann.Google Scholar
  28. Rott, H. (1992). Preferential belief change using generalized epistemic entrenchment. Journal of Logic, Language and Information, 1, 45–78.CrossRefGoogle Scholar
  29. Rott, H. (1996). Making up one’s mind. Foundations, Coherence, Nonmonotonicity, unpublished Habilitationsschrift, University of Konstanz.Google Scholar
  30. Rott, H. (2001). Change, choice and inference: A study in belief revision and nonmonotonic reasoning. Oxford: Oxford University Press.Google Scholar
  31. Rott, H. (2003). Basic entrenchment. Studia Logica, 73, 257–280.CrossRefGoogle Scholar
  32. Rott, H. (2009). Degrees all the way down: Beliefs, non-beliefs and disbeliefs. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief (pp. 301–354). Dordrecht: Springer.CrossRefGoogle Scholar
  33. Shoham, Y. (1987). A semantical approach to nonmonotonic logics. In Proceedings 2nd IEEE symposium on logic in computer science (pp. 275–279). Ithaca: IEEE Computer Society Press.Google Scholar
  34. Spohn, W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states. In W. Harper & B. Skyrms (Eds.), Causation in decision, belief change, and statistics (pp. 105–134). Dordrecht: Kluwer.Google Scholar

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of RegensburgRegensburgGermany

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