Name
Abstract | ||
|---|---|---|
In previous work [V. Biazzo, A. Gilio, T. Lukasiewicz and G. Sanfilippo, Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P, Journal of Applied Non-Classical Logics 12(2) (2002) 189---213.], we have explored the relationship between probabilistic reasoning under coherence and model-theoretic probabilistic reasoning. In particular, we have shown that the notions of g-coherence and of g-coherent entailment in probabilistic reasoning under coherence can be expressed by combining notions in model-theoretic probabilistic reasoning with concepts from default reasoning. In this paper, we continue this line of research. Based on the above semantic results, we draw a precise picture of the computational complexity of probabilistic reasoning under coherence. Moreover, we introduce transformations for probabilistic reasoning under coherence, which reduce an instance of deciding g-coherence or of computing tight intervals under g-coherent entailment to a smaller problem instance, and which can be done very efficiently. Furthermore, we present new algorithms for deciding g-coherence and for computing tight intervals under g-coherent entailment, which reformulate previous algorithms using terminology from default reasoning. They are based on reductions to standard problems in model-theoretic probabilistic reasoning, which in turn can be reduced to linear optimization problems. Hence, efficient techniques for model-theoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence (for example, column generation techniques). We describe several such techniques, which transform problem instances in model-theoretic probabilistic reasoning into smaller problem instances. We also describe a technique for obtaining a reduced set of variables for the associated linear optimization problems in the conjunctive case, and give new characterizations of this reduced set as a set of non-decomposable variables, and using the concept of random gain. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1007/s10472-005-9005-y | Ann. Math. Artif. Intell. |
Keywords | DocType | Volume |
conditional probability assessment,logical constraint,conditional constraint,probabilistic logic under coherence,model-theoretic probabilistic logic,g-coherence,g-coherent entailment,computational complexity,algorithms | Conference | 45 |
Issue | ISSN | Citations |
1-2 | 1012-2443 | 36 |
PageRank | References | Authors |
1.64 | 39 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Veronica Biazzo | 1 | 172 | 10.42 |
| Angelo Gilio | 2 | 419 | 42.04 |
| Thomas Lukasiewicz | 3 | 2618 | 165.18 |
| Giuseppe Sanfilippo | 4 | 204 | 17.14 |