Skip to main content

Degrees All the Way Down: Beliefs, Non-Beliefs and Disbeliefs

  • Chapter
Degrees of Belief

Part of the book series: Synthese Library ((SYLI,volume 342))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Buchanan, Brian G., and Edward H. Shortliffe (1984): Rule-Based Expert Systems: The MYCIN Experiment of the Stanford Heuristic Programming Project, Addison-Wesley, Readings, MA.

    Google Scholar 

  • Chellas, Brian (1980): Modal Logic. An Introduction , Cambridge: Cambridge University Press.

    Google Scholar 

  • Cohen, L. Jonathan (1977): The Probable and the Provable, Oxford: Clarendon Press.

    Google Scholar 

  • Dubois, Didier (1986): ‘Belief Structures, Possibility Theory and Decomposable Confidence Measures on Finite Sets’, Computers and Artificial Intelligence 5, 403–416.

    Google Scholar 

  • Dubois, Didier, Helene Fargier and Henri Prade (2004): ‘Ordinal and Probabilistic Representations of Acceptance’, Journal of Artificial Intelligence Research 22, 23–56.

    Google Scholar 

  • Dubois, Didier, Serafin Moral and Henri Prade (1998): ‘Belief Change Rules in Ordinal and Numerical Uncertainty Theories’, in Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 3: Belief Change, Dordrecht, Kluwer 1998, 311–392.

    Google Scholar 

  • Dubois, Didier, and Henri Prade (1988a): ‘An Introduction to Possibilistic and Fuzzy Logics’, Non-Standard Logics for Automated Reasoning, eds. Philippe Smets, Abe Mamdami, Didier Dubois and Henry Prade, London, Academic Press, 287–315.

    Google Scholar 

  • Dubois, Didier, and Henri Prade (1988b): ‘Representation and Combination of Uncertainty with Belief Functions and Possibility Measures’, Computational Intelligence 4, 244–264.

    Article  Google Scholar 

  • Dubois, Didier, and Henri Prade (1991): ‘Epistemic entrenchment and possibilistic logic’, Artificial Intelligence 50, 223–239.

    Article  Google Scholar 

  • Dubois, Didier, Henri Prade and Philippe Smets (1996): ‘Representing partial ignorance’, IEEE Transactions on System, Man, and Cybernetics, Part A: Systems and Humans 26, 361–-377.

    Article  Google Scholar 

  • Elkan, Charles (1994): ‘The Paradoxical Success of Fuzzy Logic’, IEEE Expert 9, August 1994, pp. 3–8.

    Google Scholar 

  • Foley, Richard (1992): ‘The Epistemology of Belief and the Epistemology of Degrees of Belief’, American Philosophical Quarterly 29, 111–121.

    Google Scholar 

  • Friedman, Nir, and Joseph Y. Halpern (1995): ‘Plausibility Measures: A User’s Guide with J.Y. Halpern’, Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI 95), Philippe Besnard and Steve Hanks (eds.), San Francisco, Cal., Morgan Kaufmann, pp. 175–184.

    Google Scholar 

  • Friedman, Nir, and Joseph Y. Halpern (2001): ‘Plausibility measures and default reasoning’, Journal of the ACM, 48, 648–685.

    Article  Google Scholar 

  • Gärdenfors, Peter (1988): Knowledge in Flux: Modeling the Dynamics of Epistemic States, Cambridge, Mass., Bradford Books, MIT Press.

    Google Scholar 

  • Gärdenfors, Peter, and David Makinson (1988): ‘Revisions of Knowledge Systems Using Epistemic Entrenchment’, in Moshe Vardi (ed.), Theoretical Aspects of Reasoning About Knowledge, Los Altos, CA: Morgan Kaufmann, pp. 83–95.

    Google Scholar 

  • Gärdenfors, Peter, and David Makinson (1994): ‘Nonmonotonic inference based on expectations’, Artificial Intelligence 65, 197–245.

    Article  Google Scholar 

  • Goble, Lou F. (1970): ‘Grades of Modality’, Logique et Analyse 13, No. 51, 323–334.

    Google Scholar 

  • Grove, Adam (1988): ‘Two Modellings for Theory Change’, Journal of Philosophical Logic 17, 157–170.

    Article  Google Scholar 

  • Halpern, Joseph Y. (1997): ‘Defining relative likelihood in partially-ordered preferential structures’, Journal of Artificial Intelligence Research 7, 1–-24.

    Google Scholar 

  • Halpern, Joseph Y. (2001): ‘Lexicographic probability, conditional probability, and nonstandard probability’, CoRR – The Computing Research Repository, http://arxiv.org/pdf/cs.GT/0306106.

  • Halpern, Joseph Y. (2003): Reasoning about Uncertainty, Cambridge, Mass., MIT Press.

    Google Scholar 

  • Hammond, Peter J. (1994): ‘Elementary non-Archimedean representations of probability for decision theory and games’, in Paul Humphreys (ed.), Patrick Suppes: Scientific Philosopher, Vol. 1, Dordrecht, Kluwer, pp. 25–59.

    Google Scholar 

  • Hawthorne, James, and Luc Bovens (1999): ‘The Preface, the Lottery, and the Logic of Belief’, Mind 108, 241–264.

    Article  Google Scholar 

  • Hintikka, Jaakko (1962): 1962 Jaakko Hintikka published Knowledge and Belief: An Introduction to the Logic of the Two Notions, Ithaca, Cornell University Press.

    Google Scholar 

  • Levi, Isaac (1967): Gambling with Truth, New York, Knopf.

    Google Scholar 

  • Levi, Isaac (1980): The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance, Cambridge, Mass.: MIT Press.

    Google Scholar 

  • Levi, Isaac (1984): ‘Potential surprise: its role in inference and decision making’, in I.L., Decisions and Revisions: Philosophical Essays on Knowledge and Value, Cambridge: Cambridge University Press, p. 214–242.

    Google Scholar 

  • Levi, Isaac (1991): The Fixation of Belief and Its Undoing: Changing Beliefs Through Inquiry, Cambridge: Cambridge University Press.

    Google Scholar 

  • Levi, Isaac (1996): For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference and Nonmonotonic Reasoning, Cambridge: Cambridge University Press.

    Google Scholar 

  • Levi, Isaac (2004): Mild Contraction : Evaluating Loss of Information due to Loss of Belief, Oxford: Oxford University Press.

    Google Scholar 

  • Levi, Isaac (2006): ‘Corrigibilism and Not Separatism Divides Us: Reply to Spohn’, in Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi, ed. Erik J. Olsson, Cambridge: Cambridge University Press, pp. 347–350.

    Google Scholar 

  • Lewis, David (1973): Counterfactuals, Blackwell, Oxford.

    Google Scholar 

  • Lindström, Sten, and Wlodzimierz Rabinowicz (1991), ‘Epistemic Entrenchment with Incomparabilities and Relational Belief Revision’, in André Fuhrmann and Michael Morreau (eds.), The Logic of Theory Change, Berlin, Springer, pp. 93–126.

    Chapter  Google Scholar 

  • Locke, John (1690): An Essay Concerning Human Understanding, P.H. Nidditch (ed.). Oxford: Clarendon Press, 1975.

    Google Scholar 

  • Makinson, David, and Peter Gärdenfors (1991): ‘Relations Between the Logic of Theory Change and Nonmonotonic Logic’, in André Fuhrmann and Michael Morreau (eds.), The Logic of Theory Change, Berlin, Springer, pp. 185–205.

    Google Scholar 

  • Quine, Willard V.O., and Joseph S. Ullian (1978): The Web of Belief, second edition, Random House, New York.

    Google Scholar 

  • Rabinowicz, Wlodzimierz (1995): ‘Stable Revision, or Is Preservation Worth Preserving?’, in Logic, Action and Information: Essays on Logic in Philosophy and Artificial Intelligence, eds. André Fuhrmann and Hans Rott, de Gruyter, Berlin, pp. 101–128.

    Google Scholar 

  • Rescher, Nicholas (1964): Hypothetical Reasoning, Amsterdam, North-Holland Publishing Company.

    Google Scholar 

  • Rescher, Nicholas (1976): Plausible Reasoning, van Gorcum, Assen.

    Google Scholar 

  • Rott, Hans (1991): ‘Two Methods of Constructing Contractions and Revisions of Knowledge Systems’, Journal of Philosophical Logic 20, 149–73.

    Article  Google Scholar 

  • Rott, Hans (1992): ‘Modellings for Belief Change: Prioritization and Entrenchment’, Theoria 58, 21–57.

    Article  Google Scholar 

  • Rott, Hans (2000): ‘,“Just Because”: Taking Belief Bases Seriously’, in Logic Colloquium ’98 – Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic held in Prague\/, eds. Samuel R. Buss, Petr Hájek und Pavel Pudlák, Lecture Notes in Logic, Vol. 13, Urbana, Ill.: Association for Symbolic Logic, pp. 387–408.

    Google Scholar 

  • Rott, Hans (2001): Change, Choice and Inference. Oxford University Press.

    Google Scholar 

  • Rott, Hans (2003): ‘Basic Entrenchment’, Studia Logica 73, 257–280.

    Article  Google Scholar 

  • Rott, Hans (2006): ‘The Value of Truth and the Value of Information: On Isaac Levi’s Epistemology’, in Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi, ed. Erik J. Olsson, Cambridge, Cambridge University Press, pp. 179–200.

    Google Scholar 

  • Shackle, George L.S. (1949): Expectation in Economics, Cambridge, Cambridge University Press. Second edition 1952.

    Google Scholar 

  • Shackle, George L.S. (1961): Decision, Order and Time in Human Affairs, Cambridge, Cambridge University Press.

    Google Scholar 

  • Spohn, Wolfgang (1986): ‘The Representation of Popper Measures’, Topoi 5, 69–74.

    Article  Google Scholar 

  • Spohn, Wolfgang (1988): ‘Ordinal Conditional Functions: A Dynamic Theory of Epistemic States’, in Causation in Decision, Belief Change, and Statistics, Vol. 2, eds. William L. Harper and Brian Skyrms, Dordrecht, Kluwer, pp. 105–134.

    Google Scholar 

  • Spohn, Wolfgang (1990): ‘A General Non-Probabilistic Theory of Inductive Reasoning’, in: R.D. Shachter, T.S. Levitt, J. Lemmer and L.N. Kanal (eds.), Uncertainty in Artificial Intelligence 4, Amsterdam, Elsevier, pp. 149–158.

    Google Scholar 

  • Spohn, Wolfgang (1991): ‘A Reason for Explanation: Explanations Provide Stable Reasons’, in: Wolfgang Spohn, Bas C. van Fraassen, Brian Skyrms (eds.), Existence and Explanation, Dordrecht, Kluwer, pp. 165–196.

    Google Scholar 

  • Spohn, Wolfgang (2002): ‘Laws, Ceteris Paribus Conditions, and the Dynamics of Belief’, Erkenntnis 57, 373–394.

    Article  Google Scholar 

  • Spohn, Wolfgang (2006): ‘Isaac Levi’s Potentially Surprising Epistemological Picture’, in Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi, ed. Erik J. Olsson, Cambridge, Cambridge University Press, pp. 125–142.

    Google Scholar 

  • van Fraassen, Bas C. (1976): ‘Representation of conditional probabilities’, Journal of Philosophical Logic 5, 417–-430.

    Google Scholar 

  • Wheeler, Gregory (2005): ‘On the Structure of Rational Acceptance: Comments on Hawthorne and Bovens’, Synthese 144, 287–304.

    Article  Google Scholar 

  • Williams, Mary-Anne (1995): ‘Iterated Theory Base Change: A Computational Model’, in IJCAI-95 – Proceedings of the 14th International Joint Conference on Artificial Intelligence, San Mateo, Morgan Kaufmann, pp. 1541–1550.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Rott, H. (2009). Degrees All the Way Down: Beliefs, Non-Beliefs and Disbeliefs. In: Huber, F., Schmidt-Petri, C. (eds) Degrees of Belief. Synthese Library, vol 342. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9198-8_12

Download citation

Publish with us

Policies and ethics