Abstract
The axiomatic system P is an important standard for plausible, nonmonotonic inferences that is, however, known to be too weak to solve benchmark problems like irrelevance, or subclass inheritance (so-called Drowning Problem). Spohn’s ranking functions which provide a semantic base for system P have often been used to design stronger inference relations, like Pearl’s system Z, or c-representations. While each c-representation shows excellent inference properties and handles particularly irrelevance and subclass inheritance properly, it is still an open problem which c-representation is the best. In this paper, we focus on the generic properties of c-representations and consider the skeptical inference relation (c-inference) that is obtained by taking all c-representations of a given knowledge base into account. In particular, we show that c-inference preserves the properties of solving irrelevance and subclass inheritance which are met by every single c-representation. Moreover, we characterize skeptical c-inference as a constraint satisfaction problem so that constraint solvers can be used for its implementation.
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References
Adams, E.W.: The Logic of Conditionals: An Application of Probability to Deductive Logic. Synthese Library. Springer, Dordrecht (1975)
Beierle, C., Kern-Isberner, G.: A declarative approach for computing ordinal conditional functions using constraint logic programming. In: Tompits, H., Abreu, S., Oetsch, J., Pührer, J., Seipel, D., Umeda, M., Wolf, A. (eds.) INAP/WLP 2011. LNCS (LNAI), vol. 7773, pp. 175–192. Springer, Heidelberg (2013)
Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. In: Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (IJCAI 1993), vol. 1, pp. 640–647. Morgan Kaufmann Publishers, San Francisco (1993)
Dubois, D., Prade, H.: Conditional objects as nonmonotonic consequence relations. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR 1994), pp. 170–177. Morgan Kaufmann Publishers, San Francisco (1996)
Dubois, D., Prade, H.: Possibility theory and its applications: where do we stand? In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 31–60. Springer, Heidelberg (2015)
Finetti, B.D.: Theory of Probability, vol. 1,2. Wiley, New York (1974)
Goldszmidt, M., Pearl, J.: On the consistency of defeasible databases. Artif. Intell. 52(2), 121–149 (1991)
Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artif. Intell. 84(1–2), 57–112 (1996)
Kern-Isberner, G., Eichhorn, C.: Structural inference from conditional knowledge bases. In: Unterhuber, M., Schurz, G. (eds.) Logic and Probability: Reasoning in Uncertain Environments, pp. 751–769 (2014). No. 102(4) in Studia Logica. Springer, Dordrecht (2014)
Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)
Kern-Isberner, G.: A thorough axiomatization of a principle of conditional preservation in belief revision. Ann. Math. Artif. Intell. 40, 127–164 (2004)
Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 35–110. Oxford University Press, New York (1994)
Pearl, J.: System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning About Knowledge (TARK1990), pp. 121–135. Morgan Kaufmann Publishers Inc., San Francisco (1990)
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: Proceedings of the Irvine Conference on Probability and Causation. The Western Ontario Series in Philosophy of Science, vol. 42, pp. 105–134. Springer, Dordrecht (1988)
Spohn, W.: The Laws of Belief: Ranking Theory and Its Philosophical Applications. Oxford University Press, Oxford (2012)
Thorn, P.D., Eichhorn, C., Kern-Isberner, G., Schurz, G.: Qualitative probabilistic inference with default inheritance for exceptional subclasses. In: PROGIC 2015: The Seventh Workshop on Combining Probability and Logic (2015)
Acknowledgment
This work was supported by DFG-Grant KI1413/5-1 of Prof. Dr. Gabriele Kern-Isberner as part of the priority program “New Frameworks of Rationality” (SPP 1516). Christian Eichhorn is supported by this Grant. This work benefitted very much from discussions led during Dagstuhl Seminar 15221 “Multi-disciplinary approaches to reasoning with imperfect information and knowledge - a synthesis and a roadmap of challenges”.
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Beierle, C., Eichhorn, C., Kern-Isberner, G. (2016). Skeptical Inference Based on C-Representations and Its Characterization as a Constraint Satisfaction Problem. In: Gyssens, M., Simari, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2016. Lecture Notes in Computer Science(), vol 9616. Springer, Cham. https://doi.org/10.1007/978-3-319-30024-5_4
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DOI: https://doi.org/10.1007/978-3-319-30024-5_4
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