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.
Keywords
- Probabilistic Logic
- Logical Constraint
- Classical Counterpart
- Probabilistic Generalization
- Default Reasoning
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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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. https://doi.org/10.1007/978-3-540-45062-7_47
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DOI: https://doi.org/10.1007/978-3-540-45062-7_47
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