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Probabilistic Logic under Coherence, Conditional Interpretations, and Default Reasoning

Angelo Gilio
Synthese
Vol. 146, No. 1/2, Non-Monotonic and Uncertain Reasoning in Cognition (Aug., 2005), pp. 139-152
Published by: Springer
Stable URL: http://www.jstor.org/stable/20118621
Page Count: 14
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Probabilistic Logic under Coherence, Conditional Interpretations, and Default Reasoning
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Abstract

We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give more general definitions of the notions of probabilistic consistency and probabilistic entailment of Adams. We also recall a notion of strict p-consistency and some related results. Moreover, we give new proofs of some results obtained in probabilistic default reasoning. Finally, we examine the relationships between conditional probability rankings and the notions of g-coherence and g-coherent entailment.

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