Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding |
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Authors: | Thomas Lukasiewicz |
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Institution: | 1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria, 113 I-00198, Rome, Italy 2. Institut für Informationssysteme, Technische Universit?t Wien, Favoritenstra?e 9-11, A-1040, Vienna, Austria
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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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