Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding

We present new probabilistic generalizations of Pearl’s entailment in System [50, 32] and Lehmann’s lexicographic entailment [39], called and -entailment, which are parameterized through a value that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of and , the notions of and -entailment coincide with the probabilistic notions of and -entailment recently introduced by the author in [45] and [46], respectively. We show that the notions of and -entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System ! and the property of Rational Monotonicity. Moreover, -entailment is weaker than -entailment, and both and -entailment are proper generalizations of their classical counterparts. 1Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, I-00198 Rome, Italy; e-mail: [email protected]. Alternate address: Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria; e-mail: [email protected]. Acknowledgements: This research has been supported by a Marie Curie Individual Fellowship of the European Community programme “Human Potential” under contract number HPMF-CT-2001-001286 (Disclaimer: The author is solely responsible for information communicated and the European Commission is not responsible for any views or results expressed) and by the Austrian Science Fund under project N Z29-INF. Copyright c " 2003 by the authors INFSYS RR 1843-03-02 I