Abstract Compatibility is the problem of checking whether some given probabilistic assessments have a common joint probabilistic model. When the assessments are unconditional, the problem is well established in the literature and finds a solution through the running intersection property ( RIP ). This is not the case of conditional assessments. In this paper, we study the compatibility problem in a very general setting: any possibility space, unrestricted domains, imprecise (and possibly degenerate) probabilities. We extend the unconditional case to our setting, thus generalising most of previous results in the literature. The conditional case turns out to be fundamentally different from the unconditional one. For such a case, we prove that the problem can still be solved in general by RIP but in a more involved way: by constructing a junction tree and propagating information over it. Still, RIP does not allow us to optimally take advantage of sparsity: in fact, conditional compatibility can be simplified further by joining junction trees with coherence graphs.

中文翻译：

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兼容性、合意性和运行交叉点属性

摘要 兼容性是检查某些给定的概率评估是否具有共同的联合概率模型的问题。当评估是无条件的时，问题在文献中已经很好地建立，并通过运行交叉属性 (RIP) 找到解决方案。这不是有条件评估的情况。在本文中，我们在一个非常普遍的环境中研究兼容性问题：任何可能性空间、不受限制的域、不精确（可能退化）的概率。我们将无条件情况扩展到我们的设置，从而概括了文献中的大部分先前结果。有条件的情况与无条件的情况有根本的不同。对于这种情况，我们证明了该问题通常仍然可以通过 RIP 解决，但方式更复杂：通过构建连接树并在其上传播信息。尽管如此，RIP 不允许我们最佳地利用稀疏性：事实上，可以通过将连接树与相干图连接起来进一步简化条件兼容性。