(2005) Synthese 146 (1-2).
Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding
Thomas Lukasiewicz
pp. 153-169
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.
Publication details
DOI: 10.1007/s11229-005-9082-9
Full citation:
Lukasiewicz, T. (2005). Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding. Synthese 146 (1-2), pp. 153-169.
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