Comparison of Inference Relations Defined over Different Sets of Ranking Functions
Skeptical inference in the context of a conditional knowledge base \(\mathcal R\) can be defined with respect to a set of models of \(\mathcal R\). For the semantics of ranking functions that assign a degree of surprise to each possible world, we develop a method for comparing the inference relations induced by different sets of ranking functions. Using this method, we address the problem of ensuring the correctness of approximating c-inference for \(\mathcal R\) by constraint satisfaction problems (CSPs) over finite domains. While in general, determining a sufficient upper bound for these CSPs is an open problem, for a sequence of simple knowledge bases investigated only experimentally before, we prove that using the number of conditionals in \(\mathcal R\) as an upper bound correctly captures skeptical c-inference.
- 1.Beierle, C., Eichhorn, C., Kern-Isberner, G.: Skeptical inference based on C-representations and its characterization as a constraint satisfaction problem. In: Gyssens, M., Simari, G. (eds.) FoIKS 2016. LNCS, vol. 9616, pp. 65–82. Springer, Cham (2016). doi:10.1007/978-3-319-30024-5_4 CrossRefGoogle Scholar
- 2.Beierle, C., Kutsch, S.: Regular and sufficient bounds of finite domain constraints for skeptical c-inference. In: Benferhat, S., Tabia, K., Ali, M. (eds.) Proceedings of the 30th International Conference on Industrial, Engineering, Other Applications of Applied Intelligent Systems (IEA/AIE-2017). LNAI, vol. 10350. Springer, Heidelberg (2017)Google Scholar
- 3.Beierle, C., Eichhorn, C., Kern-Isberner, G., Kutsch, S.: Properties of skeptical c-inference for conditional knowledge bases and its realization as a constraint satisfaction problem, (2017, submitted)Google Scholar
- 9.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 (TARK 1990), pp. 121–135. Morgan Kaufmann Publisher Inc., San Francisco (1990)Google Scholar
- 10.Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, II, pp. 105–134. Kluwer Academic Publishers (1988)Google Scholar