Chapter

Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Volume 2711 of the series Lecture Notes in Computer Science pp 576-587

Probabilistic Lexicographic Entailment under Variable-Strength Inheritance with Overriding

  • Thomas LukasiewiczAffiliated withDipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”

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Abstract

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 lex λ -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 lex λ -entailment.