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Probabilistic Lexicographic Entailment under Variable-Strength Inheritance with Overriding

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2711))

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.

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, I-00198, Rome, Italy

    Thomas Lukasiewicz

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  1. Thomas Lukasiewicz
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Editors and Affiliations

  1. Department of Computer Science, Aalborg University, Fredrik Bajersvej 7E, 9220, Aalborg, Denmark

    Thomas Dyhre Nielsen

  2. Department of Computer Science, Hong Kong University of Science and Technology, ClearWater Bay Road, Kowloon, Hong Kong, China,

    Nevin Lianwen Zhang

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40494-1

  • Online ISBN: 978-3-540-45062-7

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