Abstract
Conditionals (if-then-rules, default rules) are most important objects in knowledge representation and commonsense reasoning. Due to their non-classical nature, however, they are not easily dealt with. In this paper, we present a new approach to represent conditionals inductively in a possibilistic framework. The algebraic theory which underlies this approach proves to guarantee a most appropriate handling of conditional information. Moreover, this novel conditional theory is a very fundamental one, in that it can also be applied to guide possibilistic belief revision and gives rise to a new methodology to learn rules from data.
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References
S. Benferhat, D. Dubois, and H. Prade. Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence, 92:259–276, 1997.
S. Benferhat, D. Dubois, and H. Prade. Possibilistic and standard probabilistic semantics of conditional knowledge bases. Journal of Logic and Computation, 9(6):873–895, 1999.
C. Boutilier and M. Goldszmidt. Revision by conditional beliefs. In Proceedings 11th National Conference on Artificial Intelligence (AAAI’93), pages 649–654, Washington, DC., 1993.
S. Benferhat, A. Saffiotti, and P. Smets. Belief functions and default reasoning. Artificial Intelligence, 122:1–69, 2000.
P.G. Calabrese. Deduction and inference using conditional logic and probability. In I.R. Goodman, M.M. Gupta, H.T. Nguyen, and G.S. Rogers, editors, Conditional Logic in Expert Systems, pages 71–100. Elsevier, North Holland, 1991.
B. DeFinetti. Theory of Probability, volume 1,2. John Wiley and Sons, New York, 1974.
D. Dubois, I.R. Goodman, and P.G. Calabrese. Special issue on the conditional event algebra. IEEE Transactions on Systems, Man, and Cybernetics, 24(12), 1994.
D. Dubois, J. Lang, and H. Prade. Possibilistic logic. In D.M. Gabbay, C.H. Hogger, and J.A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 3, pages 439–513. Oxford University Press, 1994.
D. Dubois and H. Prade. Conditional objects and non-monotonic reasoning. In Proceedings 2nd Int. Conference on Principles of Knowledge Representation and Reasoning (KR’91), pages 175–185. Morgan Kaufmann, 1991.
D. Dubois and H. Prade. Conditioning, non-monotonic logic and nonstandard uncertainty models. In I.R. Goodman, M.M. Gupta, H.T. Nguyen, and G.S. Rogers, editors, Conditional Logic in Expert Systems, pages 115–158. Elsevier, North Holland, 1991.
D. Dubois and H. Prade. Epistemic entrenchment and possibilistic logic. Artificial Intelligence, 50:223–239, 1991.
D. Dubois and H. Prade. A survey of belief revision and updating rules in various uncertainty models. Intern. Journal of Intelligent Systems, 9:61–100, 1994.
A. Darwiche and J. Pearl. On the logic of iterated belief revision. Artificial Intelligence, 89:1–29, 1997.
N. Friedman and J.Y. Halpern. Conditional logics of belief change. In Proceedings 12th National Conference on Artificial Intelligence, AAAI-94, 1994.
J. Gebhardt and R. Kruse. Background and perspectives of possibilistic graphical models. In Proceedings First International Joint Conference on Qualitative and Quantitative Practical Reasoning, ECSQARU-FAPR’97,, pages 108–121. Springer, 1997.
M. Goldszmidt, P. Morris, and J. Pearl. A maximum entropy approach to nonmonotonic reasoning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(3):220–232, 1993.
I.R. Goodman and H.T. Nguyen. Conditional objects and the modeling of uncertainties. In M.M. Gupta and T. Yamakawa, editors, Fuzzy Computing — Theory, Hardware and Applications, pages 119–138. North-Holland, 1988.
G. Kern-Isberner. Characterizing the principle of minimum cross-entropy within a conditional-logical framework. Artificial Intelligence, 98:169–208, 1998.
G. Kern-Isberner. A unifying framework for symbolic and numerical approaches to nonmonotonic reasoning and belief revision. Department of Computer Science, FernUniversität Hagen, 1999. Habilitation thesis.
G. Kern-Isberner. Conditional preservation and conditional indifference (preliminary version). In Proceedings 8th International Workshop on Nonmonotonic Reasoning (NMR’2000), Breckenridge, Colorado, 2000.
G. Kern-Isberner. Solving the inverse representation problem. In Proceedings 14th European Conference on Artificial Intelligence, ECAI’2000, pages 581–585, Berlin, 2000. IOS Press.
G. Kern-Isberner. Conditionals in nonmonotonic reasoning and belief revision. Springer, Lecture Notes in Artificial Intelligence, 2001. (to appear).
G. Kern-Isberner. Handling conditionals adequately in uncertain reasoning. In Proceedings ECSQARU’01, 2001. (to appear).
H. Katsuno and K. Satoh. A unified view of consequence relation, belief revision and conditional logic. In Proceedings Twelfth International Joint Conference on Artificial Intelligence, IJCAI-91, pages 406–412, 1991.
D. Lewis. Probabilities of conditionals and conditional probabilities. The Philosophical Review, 85:297–315, 1976.
D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence, 55:1–60, 1992.
R.C. Lyndon and P.E. Schupp. Combinatorial group theory. Springer, Berlin Heidelberg New York, 1977.
D. Nute. Topics in Conditional Logic. D. Reidel Publishing Company, Dordrecht, Holland, 1980.
H.T. Nguyen and E.A. Walker. A history and introduction to the algebra of conditional events and probability logic. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1671–1675, 1994.
J.B. Paris. The uncertain reasoner’s companion — A mathematical perspective. Cambridge University Press, 1994.
H. Rott. A nonmonotonic conditional logic for belief revision, part I: Semantics and logic of simple conditionals. In A. Fuhrmann and M. Morreau, editors, The logic of theory change, pages 135–181. Springer, Berlin, Heidelberg, New York, 1991.
W. Spohn. Ordinal conditional functions: a dynamic theory of epistemic states. In W.L. Harper and B. Skyrms, editors, Causation in Decision, Belief Change, and Statistics, II, pages 105–134. Kluwer Academic Publishers, 1988.
E.A. Walker. Stone algebras, conditional events, and three valued logic. IEEE Transactions on Systems, Man, and Cybernetics (Special Issue on The Conditional Event Algebra), 24(12):1699–1707, 1994.
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Kern-Isberner, G. (2001). Representing and Learning Conditional Information in Possibility Theory. In: Reusch, B. (eds) Computational Intelligence. Theory and Applications. Fuzzy Days 2001. Lecture Notes in Computer Science, vol 2206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45493-4_24
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DOI: https://doi.org/10.1007/3-540-45493-4_24
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