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 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.