Probabilistic Logic under Coherence‚ Model−Theoretic Probabilistic Logic‚ and Default Reasoning
Veronica Biazzo‚ Angelo Gilio‚ Thomas Lukasiewicz and Giuseppe Sanfilippo
We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherence-based and model-theoretic probabilistic logic. Interestingly, 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. Crucially, we even show that probabilistic reasoning under coherence is a probabilistic generalization of default reasoning in system P. That is, we provide a new probabilistic semantics for system P, which is neither based on infinitesimal probabilities nor on atomic-bound (or also big-stepped) probabilities. These results also give new insight into default reasoning with conditional objects.