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Nonmonotonic Probabilistic Reasoning under Variable-Strength Inheritance with Overriding

Thomas Lukasiewicz
Synthese
Vol. 146, No. 1/2, Non-Monotonic and Uncertain Reasoning in Cognition (Aug., 2005), pp. 153-169
Published by: Springer
Stable URL: http://www.jstor.org/stable/20118622
Page Count: 17
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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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