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.
CITATION STYLE
Biazzo, V., Gilio, A., Lukasiewicz, T., & Sanfilippo, G. (2001). Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning. In Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) (Vol. 2143, pp. 290–302). Springer Verlag. https://doi.org/10.1007/3-540-44652-4_26
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