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Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding

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Abstract

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts.

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  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria, 113 I-00198, Rome, Italy

    Thomas Lukasiewicz

  2. Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Thomas Lukasiewicz

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  1. Thomas Lukasiewicz
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Lukasiewicz, T. Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding. Synthese 146, 153–169 (2005). https://doi.org/10.1007/s11229-005-9082-9

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