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Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System \(P\). (English) Zbl 1038.03023

[Extended and revised version of: Lect. Notes Comput. Sci. 2143, 290–302 (2001; Zbl 1001.68146).]
Summary: We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model-theoretic probabilistic reasoning and to default reasoning in System \(P\). In particular, we show that the notions of \(g\)-coherence and of \(g\)-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System \(P\). That is, we provide a new probabilistic semantics for System \(P\) which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System \(P\), and they give new insight into default reasoning with conditional objects.

MSC:

03B48 Probability and inductive logic
68T37 Reasoning under uncertainty in the context of artificial intelligence

Citations:

Zbl 1001.68146
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References:

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