We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherence-based and classical 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. Using these results, we analyze the computational complexity of probabilistic reasoning under coherence. Moreover, we present new algorithms for deciding g-coherence and for computing tight g-coherent intervals, which reduce these tasks to standard reasoning tasks in model-theoretic probabilistic logic. Thus, efficient techniques for model-theoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence, for example, column generation techniques. We then describe two other interesting techniques for efficient model-theoretic probabilistic reasoning in the conjunctive case.
Keywords. conditional probability assessments, probabilistic logic, g-coherence, g-coherent entailment, complexity and algorithms
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Authors addresses:
Veronica Biazzo
Citta Universitaria
Viale A. Doria 6
95152 Catania
Italy
Angelo Gilio
Via A. Scarpa 16
00161 Roma
Italy
Thomas Lukasiewicz
Favoritenstrasse 11
A-1040 Vienna
Austria
Giuseppe Sanfilippo
Citta Universitaria
Viale A. Doria 6
95152 Catania
Italy
E-mail addresses:
| Veronica Biazzo | vbiazzo@dmi.unict.it |
| Angelo Gilio | gilio@dmmm.uniroma1.it gilio@dmi.unict.it |
| Thomas Lukasiewicz | Thomas.Lukasiewicz@kr.tuwien.ac.at |
| Giuseppe Sanfilippo | gsanfilippo@dmi.unict.it |