Abstract
The notion of epistemic independence naturally arises in the framework of reasoning under uncertainty and belief change. Most prominently, probabilistic conditional independence (between variables) plays a key role in Bayesian nets. Several authors [Delgrande and Pelletier, 1994; Benferhat et al., 1994; Dubois et al., 1994; Farinas del Cerro and Herzig, 1995] have advocated the interest of qualitative independence notions for nonmonotonic reasoning. Gärdenfors [1990] has investigated the complementary notion of relevance in relation with belief change; continuing in this spirit, Farinas del Cerro and Herzig [1996] have related independence and belief contraction. In the framework of possibility theory, new forms of independence between variables have been studied by Fonck [1993], and De Campos et al. [1995], who develop possibilistic counterparts of Bayesian nets. The aim of the paper is to provide an exhaustive typology of the forms that independence and relevance can take in the setting of an ordinal approach to uncertainty. Such an approach underlies major belief change and nonmonotonic inference theories.
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References
C. E. P. Alchourron, P. Gärdenfors and D. Makinson. On the logic of theory change: Partial meet functions for contraction and revision. J. of Symbolic Logic,50 510–530, 1985.
S. Benferhat, D. Dubois and H. Prade. Representing default rules in possibilistic logic. In Proc. of the 3rd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’92), Cambridge, MA, pp. 673–6684, 1992.
S. Benferhat, D. Dubois and H. Prade. Expressing independence in a possibilistic framework and its application to default reasoning. In Proc. of the 11th Europ. Conf. on Artificial Intelligence (ECAI’94),A. G. Cohn, ed. pp. 150–154. Wiley, New York, 1994.
S. Benferhat, D. Dubois and H. Prade. Beyond counter-examples to non-monotonic formalisms: A possibility-theoretic analysis. In Proc. of the 12th Europ. Conf. on Artificial Intelligence (ECAI’96),W. Wahlster, ed. pp. 652–656. John Wiley and Sons, New York, 1996.
S. Benferhat, D. Dubois and H. Prade. Coping with the limitations of rational inference in the framework of possibility theory. In Proc of the 12th Conf. on Uncertainty in Artificial Intelligence (UAI’96),pp. 90–97, 1996.
S. Benferhat, D. Dubois and H. Prade. Nonmonotoac reasoning, conditional objects and possibility theory. Artificial Intelligence,92 259–276, 1997.
S. Benferhat, D. Dubois and H. Prade. Practical handling of exception-tainted rules and independence information in possibilistic logic. Applied Intelligence,9 101–127, 1998.
C. Boutilier. Modal logics for qualitative possibility theory. Int. J. of Approximate Reasoning, 10, 173–201, 1994.
L. M. de Campos, J. Gebhardt and R. Kruse. Axiomatic treatment of possibilistic independence. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty,C. Froidevaux and J. Kohlas, eds. pp. 77–88. LNAI 946, Springer Verlag, Berlin, 1995.
J. P. Delgrande and J. Pelletier. A formal approach to relevance. Tech. Report, Simon Fraser University, Burnaby, BC, Canada, 1994
D. Dubois. Belief structures, possibility theory, decomposable confidence measures on finite sets. Computer and Artificial Intelligence, 5, 403–417, 1986.
D. Dubois, L. Farinas del Cerro, A. Herzig and H. Prade. An ordinal view of independence with application to plausible reasoning. In Proc. of the 10th Conf. on Uncertainty in Artificial Intelligence, R. Lopez de Mantaras and D. Poole, eds. pp. 195–203. Seattle, WA, 1994.
D. Dubois, L. Farifias del Cerro, A. Herzig, H. Prade. Qualitative independence: a roadmap. In Proc. Inter. Conf. on Artificial Intelligence (MCAT 97), pp. 62–67. Nagoya, Japan, 1997.
D. Dubois and H. Prade. Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, 1988.
D. Dubois and H. Prade. Epistemic entrenchment and possibilistic logic. Artificial Intelligence, 50, 223–239, 1991.
D. Dubois, H. Prade. (1992), Belief change and possibility theory. In Belief Revision, P. Gärdenfors, ed. pp. 142–182. Cambridge University Press, 1992.
D. Dubois and H. Prade. Conditional objects as nonmonotonic consequence relations -Main results. In Proc. of the 4th Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’94), J. Doyle, E. Sandewall and P. Torasso, eds. pp. 170–177. Morgan Kaufmann, San Mateo, CA, 1994.
D. Dubois and H. Prade. Conditional objects, possibility theory and default rules. In Conditionals: From Philosophy to Computer Sciences, G. Crocco, L. Farinas del Cerro and A. Herzig, eds. pp. 311–346. Oxford University Press, 1995.
D. Dubois and H. Prade. Numerical representations of acceptance. In Proc. of the 11th Conf. on Uncertainty in Artificial Intelligence, P. Besnard, S. Hanks, eds. pp. 149–156, 1995.
D. Dubois and H. Prade. Possibility theory: qualitative an quantitative aspects. In Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol 1, (P. Smets, Ed). Kluwer Academic Publishers, Dordrecht, pp. 169–226, 1998.
L. Farinas del Cerro and A. Herzig. A modal analysis of possibility theory. In Proc. of the Inter. Workshop on Fundamentals of Artificial Intelligence Research (FAIR’9I), Ph. Jorrand and J. Kelemen, eds. pp. 11–18. LNCS 535, Springer Verlag, Berlin, 1991.
L. Farinas del Cerro and A. Herzig. Possibility theory and independence. In Advances in Intelligent Computing - IPMU’94 (Selected Papers of the 5th Inter. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, B. Bouchon-Meunier, R. R. Yager and L. A. Zadeh, eds. pp. 292–301. Lecture Notes in Computer Science, Vol. 945, Springer Verlag, Berlin, 1995.
L. Farinas del Cerro and A. Herzig. Belief change and dependence. In Pmc. of the 6th Conf on Theoretical Aspects of Rationality and Knowledge (TARK’96), Y. Shoham, ed. pp. 147–161. Morgan Kaufmann, San Francisco, CA, 1996.
L. Farinas del Cerro, A. Herzig and J. Lang. From ordering-based nonmonotonic reasoning to conditional logics. Artificial Intelligence,66 375–393, 1994.
T. Fine. Theories of Probability. Academic Press, New York, 1973.
P. Fonck. Réseaux d’ inférence pour le raisonnement possibiliste. Dissertation, Université de Liége, Belgium, 1993.
P. Gärdenfors. Knowledge in Flux - Modeling the Dynamics of Epistemic States. The MIT Press, Cambridge, MA, 1988.
P. Gärdenfors. On the logic of relevance. In Philosophy of Probability, J. P. Dubucs, ed. pp. 35–43. Kluwer Academic Publ., Dordrecht, 1993.
P. Gärdenfors and D. Makinson. Revisions of knowledge systems using epistemic entrenchment. In Proc. of the 2nd Conf. on Theoretical Aspects of Reasoning About Knowledge, M.Y. Vardi, ed. pp. 83–95. Morgan Kaufmann, Los Altos, CA, 1988.
P. Gärdenfors and D. Makinson. Non-monotonic inference based on expectations. Artificial Intelligence, 65, 197–245, 1994.
M. Goldszmidt and J. Pearl. Rank-based systems: A simple approach to belief revision, belief update, and reasoning about evidence and actions. In Proc. of the 3rd Inter. Conf. on Principles of Knowledge Representation and Reasoning (KR’92), B. Nebel, et al. eds. pp. 661–672. Morgan Kaufmann, San Mateo, 1992.
P. Hajek, D. Harmankova and R. Verbrugge. A qualitative fuzzy possibilistic logic. Int. J. ofApprox. Reas.,12 1–19,1994.
J. M. Keynes. A Treatise on Probability. MacMillan, London, 1921.
A. Kolmogorov. Foundations of the Theory of Probability. Chelsea, Bronx, New York, 1956.
S. Kraus, D. Lehmann and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence,44 167–207, 1990.
D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence, 55, 1–60, 1992.
D. Lewis. Counterfactuals. 2nd edition, Billing and Sons Ltd., Worcester, UK, 1986.
J. Paris. The Uncertain Reasoner’s Companion - A Mathematical Perspective. Cambridge University Press, Cambridge, UK, 1994.
G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, NJ, 1976.
Y. Shoham. Reasoning About Change - Time and Causation from the Standpoint of Artificial Intelligence. The MIT Press, Cambridge, MA, 1988.
W. Spohn. Ordinal conditional functions: a dynamic theory of epistemic states. In Causation in Decision, Belief Change and Statistics, W. Harper, B. Skyrms, eds. pp. 105–134, 1988.
L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28, 1978.
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Dubois, D., Del Cerro, L.F., Herzig, A., Prade, H. (1999). A Roadmap of Qualitative Independence. In: Dubois, D., Prade, H., Klement, E.P. (eds) Fuzzy Sets, Logics and Reasoning about Knowledge. Applied Logic Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1652-9_22
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