Probabilistic Lexicographic Entailment under Variable-Strength Inheritance with Overriding
- Cite this paper as:
- Lukasiewicz T. (2003) Probabilistic Lexicographic Entailment under Variable-Strength Inheritance with Overriding. In: Nielsen T.D., Zhang N.L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2003. Lecture Notes in Computer Science, vol 2711. Springer, Berlin, Heidelberg
In previous work, I have presented approaches to nonmonotonic probabilistic reasoning, which is a probabilistic generalization of default reasoning from conditional knowledge bases. In this paper, I continue this exciting line of research. I present a new probabilistic generalization of Lehmann’s lexicographic entailment, called lexλ-entailment, which is parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. Roughly, the new notion of entailment is obtained from logical entailment in model-theoretic probabilistic logic by adding (i) the inheritance of purely probabilistic knowledge of strength λ, and (ii) a mechanism for resolving inconsistencies due to the inheritance of logical and purely probabilistic knowledge. I also explore the semantic properties of lexλ-entailment.
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