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A Survey of Ranking Theory

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Degrees of Belief

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References

  • Bacon, F. (1620), Novum Organum.

    Google Scholar 

  • Brafman, R.I., M. Tennenholtz (2000), “An Axiomatic Treatment of Three Qualitative Decision Criteria”, Journal of the Association of Computing Machinery 47, 452–482.

    Google Scholar 

  • Carnap, R. (1950), Logical Foundations of Probability, Chicago University Press, Chicago.

    Google Scholar 

  • Cohen, L.J. (1970), The Implications of Inductionss Methuen, London.

    Google Scholar 

  • Cohen, L.J. (1977), The Probable and the Provable, Oxford University Press, Oxford.

    Google Scholar 

  • Cohen, L.J. (1980), “Some Historical Remarks on the Baconian Conception of Probability”, Journal of the History of Ideas 41, 219–231.

    Article  Google Scholar 

  • Darwiche, A., J. Pearl (1997), “On the Logic of Iterated Belief Revision”, Artificial Intelligence 89, 1–29.

    Article  Google Scholar 

  • Dawid, A.P. (1979), “Conditional Independence in Statistical Theory”, Journal of the Royal Statistical Society B 41, 1–31.

    Google Scholar 

  • de Finetti, B. (1937), “La Prévision: Ses Lois Logiques, Ses Sources Subjectives”, Annales de l’Institut Henri Poincaré 7; engl. translation: “Foresight: Its Logical Laws, Its Subjective Sources”, in: H.E. Kyburg Jr., H.E. Smokler (eds.), Studies in Subjective Probability, Wiley, New York 1964, pp. 93–158.

    Google Scholar 

  • Dempster, A.P. (1967), “Upper and Lower Probabilities Induced by a Multivalued Mapping”, Annals of Mathematical Statistics 38, 325–339.

    Article  Google Scholar 

  • Dempster, A.P. (1968), “A Generalization of Bayesian Inference”, Journal of the Royal Statistical Society, Series B, 30, 205–247.

    Google Scholar 

  • Dubois, D., H. Prade (1988), Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, New York.

    Google Scholar 

  • Dubois, D., H. Prade (1995), “Possibility Theory as Basis for Qualitative Decision Theory”, in: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI’95), Montreal, pp. 1925–1930.

    Google Scholar 

  • Dubois, D., H. Prade (1998), “Possibility Theory: Qualitative and Quantitative Aspects”, in: D.M. Gabbay, P. Smets (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1, Kluwer, Dordrecht, pp. 169–226.

    Google Scholar 

  • Gabbay, D.M., et al. (eds.) (1994), Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3, Nonmonotonic Reasoning and Uncertainty Reasoning, Oxford University Press, Oxford.

    Google Scholar 

  • Garber, D. (1980), “Field and Jeffrey Conditionalization”, Philosophy of Science 47, 142–145.

    Article  Google Scholar 

  • Gärdenfors, P. (1978), “Conditionals and Changes of Belief”, in: I. Niiniluoto, R. Tuomela (eds.), The Logic and Epistemology of Scientific Change, North-Holland, Amsterdam, pp. 381–404.

    Google Scholar 

  • Gärdenfors, P. (1988), Knowledge in Flux, MIT Press, Cambridge, Mass.

    Google Scholar 

  • Geiger, D., J. Pearl (1990), “On the Logic of Causal Models”, in: R.D. Shachter, T.S. Levitt, J. Lemmer, L.N. Kanal (eds.), Uncertainty in Artificial Intelligence 4, Elsevier, Amsterdam, pp. 3–14.

    Google Scholar 

  • Giang, P.G., P.P. Shenoy (1999), “On Transformations Between Probability and Spohnian Disbelief Functions”, in: K.B. Laskey, H. Prade (eds.), Uncertainty in Artificial Intelligence, Vol. 15, Morgan Kaufmann, San Francisco, pp. 236–244.

    Google Scholar 

  • Giang, P.G., P.P. Shenoy (2000), “A Qualitative Linear Utility Theory for Spohn’s Theory of Epistemic Beliefs”, in: C. Boutilier, M. Goldszmidt (eds.), Uncertainity in Artificial Intelligence, Vol. 16, Morgan Kaufmann, San Francisco, pp. 220–229.

    Google Scholar 

  • Giang, P.G., P.P. Shenoy (2005), “Two Axiomatic Approaches to Decision Making Using Possibility Theory”, European Journal of Operational Research 162, 450–467.

    Article  Google Scholar 

  • Gilboa, I. (1987), “Expected Utility with Purely Subjective Non-Additive Probabilities”, Journal of Mathematical Economics 16, 65–88.

    Google Scholar 

  • Goldszmidt, M., J. Pearl (1996), “Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling”, Artificial Intelligence 84, 57–112.

    Article  Google Scholar 

  • Hacking, I. (1975), The Emergence of Probability, Cambridge University Press, Cambridge.

    Google Scholar 

  • Halpern, J.Y. (2003), Reasoning About Uncertainty, MIT Press, Cambridge, Mass.

    Google Scholar 

  • Hansson, S.O. (ed.) (1997), “Special Issue on Non-Prioritized Belief Revision”, Theoria 63, 1–134.

    Google Scholar 

  • Hansson, S.O. (1999), A Textbook of Belief Dynamics. Theory Change and Database Updating, Kluwer, Dordrecht.

    Google Scholar 

  • Harper, W.L. (1976), “Rational Belief Change, Popper Functions and Counterfactuals”, in: W.L. Harper, C.A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. I, Reidel, Dordrecht, pp. 73–115.

    Google Scholar 

  • Hempel, C.G. (1945), “Studies in the Logic of Confirmation”, Mind 54, 1–26, 97–121.

    Article  Google Scholar 

  • Hempel, C.G. (1962), “Deductive-Nomological vs. Statistical Explanation”, in: H. Feigl, G. Maxwell (eds.), Minnesota Studies in the Philosophy of Science, Vol. III, Scientific Explanation, Space, and Time, University of Minnesota Press, Minneapolis, pp. 98–169.

    Google Scholar 

  • Hild, M. (t.a.), Introduction to Induction: On the First Principles of Reasoning, Manuscript.

    Google Scholar 

  • Hild, M., W. Spohn (2008), “The Measurement of Ranks and the Laws of Iterated Contraction”, Artificial Intelligence 172, 1195–1218.

    Article  Google Scholar 

  • Hintikka, J. (1962), Knowledge and Belief, Cornell University Press, Ithaca, N.Y.

    Google Scholar 

  • Hisdal, E. (1978), “Conditional Possibilities – Independence and Noninteractivity”, Fuzzy Sets and Systems 1, 283–297.

    Article  Google Scholar 

  • Huber, F. (2006), “Ranking Functions and Rankings on Languages”, Artificial Intelligence 170, 462–471.

    Article  Google Scholar 

  • Huber, F. (2007), “The Consistency Argument for Ranking Functions”, Studia Logica 86, 299–329.

    Article  Google Scholar 

  • Hunter, D. (1991), “Graphoids, Semi-Graphoids, and Ordinal Conditional Functions”, International Journal of Approximate Reasoning 5, 489–504.

    Article  Google Scholar 

  • Jaffray, J.-Y. (1989), “Linear Utility Theory for Belief Functions”, Operations Research Letters 8, 107–112.

    Article  Google Scholar 

  • Jeffrey, R.C. (1965), The Logic of Decision, University of Chicago Press, Chicago, 2nd ed. 1983.

    Google Scholar 

  • Jeffrey, R.C. (1991), Probability and the Art of Judgment, Cambridge University Press, Cambridge.

    Google Scholar 

  • Jensen, F.V. (2001), Bayesian Networks and Decision Graphs, Springer, Berlin.

    Google Scholar 

  • Joyce, J. (1998), “A Nonpragmatic Vindication of Probabilism”, Philosophy of Science 65, 575–603.

    Article  Google Scholar 

  • Joyce, J. (1999), The Foundations of Causal Decision Theory, Cambridge University Press, Cambridge.

    Google Scholar 

  • Krantz, D.H., R.D. Luce, P. Suppes, A. Tversky (1971), Foundations of Measurement, Vol. I, Academic Press, New York.

    Google Scholar 

  • Krüger, L., et al. (1987), The Probabilistic Revolution. Vol. 1: Ideas in History, Vol. 2: Ideas in the Sciences, MIT Press, Cambridge, Mass.

    Google Scholar 

  • Kyburg, H.E. Jr. (1961), Probability and the Logic of Rational Belief, Wesleyan University Press, Middletown, Conn.

    Google Scholar 

  • Lange, M. (2000), Natural Laws in Scientific Practice, Oxford University Press, Oxford.

    Google Scholar 

  • Levi, I. (1967), Gambling with Truth, A. A. Knopf, New York.

    Google Scholar 

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

    Google Scholar 

  • Lewis, D. (1969), Convention: A Philosophical Study, Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Lewis, D. (1973), Counterfactuals, Blackwell, Oxford.

    Google Scholar 

  • Lewis, D. (1975), “Languages and Language”, in: K. Gunderson (ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, University of Minnesota Press, Minneapolis, pp. 3–35.

    Google Scholar 

  • Lewis, D. (1980), “A Subjectivist’s Guide to Objective Chance”, in: R.C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Vol II, University of California Press, Berkeley, pp. 263–293.

    Google Scholar 

  • Luce, R.D., H. Raiffa (1957), Games and Decisions, Wiley, New York.

    Google Scholar 

  • Maher, P. (2002), “Joyce’s Argument for Probabilism”, Philosophy of Science 69, 73–81.

    Article  Google Scholar 

  • Merin, A. (2006), Decision Theory of Rhetoric, book manuscript, to appear.

    Google Scholar 

  • Merin, A. (2008), “Relevance and Reasons in Probability and Epistemic Ranking Theory. A Study in Cognitive Economy”, in: Forschungsberichte der DFG-Forschergruppe Logik in der Philosophie Nr. 130, University of Konstanz.

    Google Scholar 

  • McGee, V. (1994), “Learning the Impossible”, in: E. Eells, B. Skyrms (eds.), Probability and Conditionals. Belief Revision and Rational Decision, Cambridge University Press, Cambridge, pp. 179–199.

    Google Scholar 

  • Neapolitan, R.E. (1990), Probabilistic Reasoning in Expert Systems: Theory and Algorithms, Wiley, New York.

    Google Scholar 

  • Oddie, G. (2001), “Truthlikeness”, in: E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2001 Edition),http://plato.stanford.edu/archives/fall2001/entries/truthlikeness

  • Pearl, J. (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufman, San Mateo, Ca.

    Google Scholar 

  • Pearl, J. (2000), Causality: Models, Reasoning, and Inference, Cambridge University Press, Cambridge.

    Google Scholar 

  • Plantinga, A. (1993), Warrant: The Current Debate, Oxford University Press, Oxford.

    Google Scholar 

  • Pollock, J.L. (1995), Cognitive Carpentry, MIT Press, Cambridge, MA.

    Google Scholar 

  • Rescher, N. (1964), Hypothetical Reasoning, North-Holland, Amsterdam.

    Google Scholar 

  • Rescher, N. (1976), Plausible Reasoning, Van Gorcum, Assen.

    Google Scholar 

  • Rott, H. (2001), Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, Oxford University Press, Oxford.

    Google Scholar 

  • Rott, H. (2008), “Shifting Priorities: Simple Representations for Twenty Seven Iterated Theory Change Operators”, to appear in: D. Makinson, J. Malinowski, H. Wansing (eds.), Towards Mathematical Philosophy, Springer, Dordrecht.

    Google Scholar 

  • Sarin, R., P.P. Wakker (1992), “A Simple Axiomatization of Nonadditive Expected Utility”, Econometrica 60, 1255–1272.

    Article  Google Scholar 

  • Schmeidler, D. (1989), “Subjective Probability and Expected Utility Without Additivity”, Econometrica 57, 571–587.

    Article  Google Scholar 

  • Shackle, G.L.S. (1949), Expectation in Economics, Cambridge University Press, Cambridge.

    Google Scholar 

  • Shackle, G.L.S. (1969), Decision, Order and Time in Human Affairs, Cambridge University Press, Cambridge, 2nd ed.

    Google Scholar 

  • Shafer, G. (1976), A Mathematical Theory of Evidence, Princeton University Press, Princeton.

    Google Scholar 

  • Shafer, G. (1978), “Non-Additive Probabilities in the Work of Bernoulli and Lambert”, Archive for History of Exact Sciences 19, 309–370.

    Article  Google Scholar 

  • Shenoy, P.P. (1991), “On Spohn’s Rule for Revision of Beliefs”, International Journal of Approximate Reasoning 5, 149–181.

    Article  Google Scholar 

  • Smets, P. (1998), “The Transferable Belief Model for Quantified Belief Representation”, in: D.M. Gabbay, P. Smets (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1, Kluwer, Dordrecht, pp. 267–301.

    Google Scholar 

  • Spirtes, P., C. Glymour, R. Scheines (1993), Causation, Prediction, and Search, Springer, Berlin, 2nd ed.

    Google Scholar 

  • Spohn, W. (1976/1978), Grundlagen der Entscheidungstheorie, Ph.D. Thesis, University of Munich 1976, published: Kronberg/Ts.: Scriptor 1978, out of print, pdf-version at: http://www.uni-konstanz.de/FuF/Philo/Philosophie/philosophie/files/ge.buch.gesamt.pdf.

  • Spohn, W. (1983), Eine Theorie der Kausalität, unpublished Habilitationsschrift, Universität München, pdf-version at:http://www.uni-konstanz.de/FuF/Philo/Philosophie/philosophie/files/ habilitation.pdf

  • Spohn, W. (1986), “The Representation of Popper Measures”, Topoi 5, 69–74.

    Article  Google Scholar 

  • 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, Vol. II, Kluwer, Dordrecht, pp. 105–134.

    Google Scholar 

  • Spohn, W. (1990), “A General Non-Probabilistic Theory of Inductive Reasoning”, in: R.D. Shachter, T.S. Levitt, J. Lemmer, L.N. Kanal (eds.),Uncertainty in Artificial Intelligence, Vol. 4, Elsevier, Amsterdam, pp. 149–158.

    Google Scholar 

  • Spohn, W. (1991), “A Reason for Explanation: Explanations Provide Stable Reasons”, in: W. Spohn, B.C. van Fraassen, B. Skyrms (eds.), Existence and Explanation, Kluwer, Dordrecht, pp. 165–196.

    Google Scholar 

  • Spohn, W. (1993), “Causal Laws are Objectifications of Inductive Schemes”, in: J. Dubucs (ed.), Philosophy of Probability, Kluwer, Dordrecht, pp. 223–252.

    Google Scholar 

  • Spohn, W. (1994a), “On the Properties of Conditional Independence”, in: P. Humphreys (ed.), Patrick Suppes: Scientific Philosopher. Vol. 1: Probability and Probabilistic Causality, Kluwer, Dordrecht, pp. 173–194.

    Google Scholar 

  • Spohn, W. (1994b), “On Reichenbach’s Principle of the Common Cause”, in: W.C. Salmon, G. Wolters (eds.), Logic, Language, and the Structure of Scientific Theories, Pittsburgh University Press, Pittsburgh, pp. 215–239.

    Google Scholar 

  • Spohn, W. (1999), “Two Coherence Principles”, Erkenntnis 50, 155–175.

    Article  Google Scholar 

  • Spohn, W. (2001a), “Vier Begründungsbegriffe”, in: T. Grundmann (ed.), Erkenntnistheorie. Positionen zwischen Tradition und Gegenwart, Mentis, Paderborn, pp. 33–52.

    Google Scholar 

  • Spohn, W. (2001b), “Bayesian Nets are All There is to Causal Dependence”, in: M.C. Galavotti, P. Suppes, D. Costantini (eds.), Stochastic Dependence and Causality, CSLI Publications, Stanford, pp. 157–172.

    Google Scholar 

  • Spohn, W. (2002), “Laws, Ceteris Paribus Conditions, and the Dynamics of Belief”, Erkenntnis 57, 373–394; also in: J. Earman, C. Glymour, S.Mitchell (eds.), Ceteris Paribus Laws, Kluwer, Dordrecht, pp. 97–118.

    Google Scholar 

  • Spohn, W. (2005a), “Enumerative Induction and Lawlikeness”, Philosophy of Science 72, 164–187.

    Article  Google Scholar 

  • Spohn, W. (2005b), “Isaac Levi’s Potentially Surprising Epistemological Picture”, to appear in: E. Olsson (ed.), Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi, Cambridge University Press, Cambridge.

    Google Scholar 

  • Spohn, W. (2006), “Causation: An Alternative”, British Journal for the Philosophy of Science 57, 93–119.

    Article  Google Scholar 

  • Studeny, M. (1989), “Multiinformation and the Problem of Characterization of Conditional Independence Relations”, Problems of Control and Information Theory 18, 3–16.

    Google Scholar 

  • Wakker, P.P. (2005), “Decision-Foundations for Properties of Nonadditive Measures: General State Spaces or General Outcome Spaces”, Games and Economic Behavior 50, 107–125.

    Article  Google Scholar 

  • Williamson, T. (1994), Vagueness, Routledge, London.

    Google Scholar 

  • Zadeh, L.A. (1975), “Fuzzy Logics and Approximate Reasoning”, Synthese 30, 407–428.

    Article  Google Scholar 

  • Zadeh, L.A. (1978), “Fuzzy Sets as a Basis for a Theory of Possibility”, Fuzzy Sets and Systems 1, 3–28.

    Article  Google Scholar 

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Spohn, W. (2009). A Survey of Ranking Theory. 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_8

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