## Probabilistic Logic under Coherence: Complexity and Algorithms (2001)

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Venue: | In Proceedings ISIPTA-01 |

Citations: | 22 - 11 self |

### BibTeX

@INPROCEEDINGS{Biazzo01probabilisticlogic,

author = {Veronica Biazzo and Angelo Gilio and Thomas Lukasiewicz},

title = {Probabilistic Logic under Coherence: Complexity and Algorithms},

booktitle = {In Proceedings ISIPTA-01},

year = {2001},

pages = {51--61}

}

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### 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 classical modeltheoretic 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.