Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P

Abstract

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 modeltheoretic 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.