Abstract
This paper bridges the gap between comparative belief structures, such as those induced by probability measures, and logical representations of accepted beliefs. We add, to natural properties of comparative belief relations, some conditions that ensure that accepted beliefs form a deductively closed set. It is shown that the beliefs accepted by an agent in all contexts can always be described by a family of conditionals. These results are closely connected to the nonmonotonic ’preferential’ inference system of Kraus, Lehmann and Magidor and the works of Friedman and Halpern on their so-called plausibility functions. Acceptance relations are also another way of approaching the theory of belief change after the works of Gärdenfors and colleagues.
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References
Adams, E.W.: The Logic of Conditionals. D. Reidel, Dordrecht (1975)
Alchourrón, C.E.P., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet functions for contraction and revision. J. of Symbolic Logic 50, 513–530 (1985)
Benferhat, S., Dubois, D., Prade, H.: Representing default rules in possibilistic logic. In: Proc. of the 3rd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR 1992), Cambridge, MA, pp. 673–684 (1992)
Benferhat, S., Dubois, D., Prade, H.: Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence 92, 259–276 (1997)
Benferhat, S., Dubois, D., Prade, H.: Possibilistic and standard probabilistic semantics of conditional knowledge. Journal of Logic and Computation 9, 873–895 (1999)
Benferhat, S., Dubois, D., Papini, O.: A sequential reversible belief revision method based on polynomials. In: Proceedings National American AI conference (AAAI 1999), Orlando, Floride (USA), pp. 733–738. AAAI Press/The MIT Press (1999)
Benferhat, S., Dubois, D., Lagrue, S., Prade, H.: A big-stepped probability approach for discovering default rules. In: Proc. of the Ninth Int. Conf. Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2002), Annecy, France, pp. 283–289 (2002); A revised version is to appear in the Int. J. Uncertainty, Fuzziness and Knowledge- based Systems
Boutilier, C., Goldszmidt, M.: Revision by conditionals beliefs. In: Crocco, G., Fariñas del Cerro, L., Herzig, A. (eds.) Conditionals: From Philosophy to Computer Sciences, pp. 267–300. Oxford University Press, Oxford (1995)
Calabrese, P.: An algebraic synthesis of the foundations of logic and probability. Information Sciences 42, 187–237 (1987)
Cohen, L.J.: The Probable and the Provable. Clarendon Press, Oxford (1977)
Cohen, L.J.: Belief and acceptance. Mind XCVIII(391), 367–390 (1989)
Darwishe, A., Pearl, J.: On the logic of iterated belief revision. Artificial Intelligence 89, 1–29 (1997)
Dubois, D.: Belief structures, possibility theory and decomposable confidence measures on finite sets. Computers and Artificial Intelligence (Bratislava) 5(5), 403–416 (1986)
Dubois, D., Fargier, H., Prade, H.: Comparative uncertainty, belief functions and accepted beliefs. In: Proc. of 14th Conf. on Uncertainty in Artificial Intelligence (UAI 1998), Madison, Wi, pp. 113–120 (1998)
Dubois, D., Fargier, H., Prade, H.: Ordinal and numerical representations of acceptance. Research report 02-20R, IRIT, Toulouse (2002)
Dubois, D., Moral, S., Prade, H.: Belief change rules in ordinal and numerical uncertainty theories. In: Dubois, D., Prade, H. (eds.) Belief Change, Handbook on Defeasible Reasoning and Uncertainty Management Systems, vol. 3, pp. 311–392. Kluwer Academic Publ., Dordrecht (1998)
Dubois, D., Prade, H.: Epistemic entrenchment and possibilistic logic. Artificial Intelligence 50, 223–239 (1991)
Dubois, D., Prade, H.: Conditional objects as non-monotonic consequence relationships. IEEE Trans. on Systems, Man and Cybernetics 24, 1724–1740 (1994)
Dubois, D., Prade, H.: Conditional objects, possibility theory and default rules. In: Crocco, G., Farinas del Cerro, L., Herzig, A. (eds.) Conditionals: From Philosophy to Computer Science, pp. 311–346. Oxford University Press, Oxford (1995)
Dubois, D., Prade, H.: Numerical representation of acceptance. In: Proc. of the 11th Conf. on Uncertainty in Artificial Intelligence, Montréal, Quebec, pp. 149–156 (1995)
Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Smets, P. (ed.) Quantified Representations of Uncertainty and Imprecision. Handbook on Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer Academic Publ., Dordrecht (1998)
Fariñas del Cerro, L., Herzig, A.: A modal analysis of possibility theory. In: Jorrand, P., Kelemen, J. (eds.) FAIR 1991. LNCS, vol. 535, p. 255. Springer, Heidelberg (1991)
Fishburn, P.: The axioms of subjective probability. Statistical Science 1, 335–358 (1986)
Friedman, N., Halpern, J.: Plausibility measures and default reasoning. In: Proc. of the 13th National Conf. on Artificial Intelligence (AAAI 1996), Portland, OR, pp. 1297–1304 (1996)
Gärdenfors, P.: Knowledge in Flux. MIT press, Cambridge (1988)
Goodman, I.R., Nguyen, H.T., Walker, E.A.: Conditional Inference and Logic for Intelligent Systems: a Theory of Measure-Free Conditioning. North-Holland, Amsterdam (1991)
Grove, A.: Two modellings for theory change. J. Philos. Logic 17, 157–170 (1988)
Halpern, J.: Defining relative likelihood in partially-ordered preferential structures. J. AI Research 7, 1–24 (1997)
Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087, p. 27. Springer, Heidelberg (2001)
Kraft, C.H., Pratt, J.W., Seidenberg, A.: Intuitive probability on finite sets. Ann. Math. Stat. 30, 408–419 (1959)
Kraus, K., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207 (1990)
Kyburg, H.E.: Probability and the Logic of Rational Belief. Wesleyan University Press, Middletown (1961)
Kyburg, H.E.: Knowledge. In: Lemmer, J.F., Kanal, L.N. (eds.) Uncertainty in Artificial intelligence, pp. 263–272. Elsevier, Amsterdam (1988)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence, vol. 55(1), pp. 1–60 (1992)
Lehmann, D.: Belief revision, revised. In: Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence (IJCAI 1995), Montreal, Quebec, pp. 1534–1540 (1995)
Lewis, D.L.: Counterfactuals. Basil Blackwell, Oxford (1973)
Makinson, D., Gärdenfors, P.: Relations between the logic of theory change and nonmonotonic reasoning. In: Fuhrmann, A., Morreau, M. (eds.) The Logic of Theory Change. LNCS(LNAI), vol. 465, pp. 185–205. Springer, Heidelberg (1991)
Paris, J.: The Uncertain Reasoner’s Companion. Cambridge University Press, Cambridge (1994)
Pearl, J.: Probabilistic Reasoning Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)
Pearl, J.: System Z: a natural ordering of defaults with tractable applications to default reasoning. In: Proc. of the 3rd Conf. on the Theoretical Aspects of Reasoning About Knowledge (TARK 1990), pp. 121–135. Morgan and Kaufmann, San Mateo (1990)
Poole, D.: The effect of knowledge on belief: conditioning, specificity and the lottery paradox in defaut reasoning. Artificial Intelligence 49, 281–307 (1991)
Roubens, M., Vincke, P.: Preference Modelling. Lecture Notes in Economics and Mathematical Systems, vol. 250. Springer, Berlin (1985)
Snow, P.: Diverse confidence levels in a probabilistic semantics for conditional logics. Artificial Intelligence 113, 269–279 (1999)
Spohn, W.: Ordinal conditional functions: A dynamic theory of epistemic states. In: Harper, W.L., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, vol. 2, pp. 105–134. D. Reidel, Dordrecht (1988)
Williams, M.A.: Transmutations of knowledge systems. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) Proc. of the 4th Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR 1994), Bonn, Germany, pp. 619–629 (1994)
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Dubois, D., Fargier, H., Prade, H. (2005). Acceptance, Conditionals, and Belief Revision. In: Kern-Isberner, G., Rödder, W., Kulmann, F. (eds) Conditionals, Information, and Inference. WCII 2002. Lecture Notes in Computer Science(), vol 3301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408017_3
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DOI: https://doi.org/10.1007/11408017_3
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