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Probabilistic Logic under Coherence‚ Model−Theoretic Probabilistic Logic‚ and Default Reasoning

Veronica Biazzo‚ Angelo Gilio‚ Thomas Lukasiewicz and Giuseppe Sanfilippo

Abstract

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.

Book Title
Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty‚ ECSQARU 2001‚ Toulouse‚ France‚ September 19−21‚ 2001
Editor
Salem Benferhat and Philippe Besnard
ISBN
3−540−42464−4
Pages
290−302
Publisher
Springer
Series
Lecture Notes in Computer Science
Volume
2143
Year
2001