摘要翻译：
本文介绍了一个格论框架，它允许研究与离散概率测度类有关的条件独立性蕴涵问题。将半格与CI语句联系起来，给出了一个有限的、健全的、完备的半格包含推理系统。结果表明，该系统（1）对于饱和CI语句是完整的，(2)对于一般CI语句是完整的，(3)对于稳定CI语句是完整的。这些结果给出了一个可以用来证伪蕴涵问题实例的判据，并导出了几个在多项式时间内逼近这个“格排斥”判据的启发式。最后，我们提供了实验结果，将我们的工作与其他已有的推理算法的结果联系起来。
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英文标题：
《On the Conditional Independence Implication Problem: A Lattice-Theoretic
  Approach》
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作者：
Mathias Niepert, Dirk Van Gucht and Marc Gyssens
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最新提交年份：
2008
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Discrete Mathematics        离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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英文摘要：
  A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a finite, sound and complete inference system relative to semi-lattice inclusions is presented. This system is shown to be (1) sound and complete for saturated CI statements, (2) complete for general CI statements, and (3) sound and complete for stable CI statements. These results yield a criterion that can be used to falsify instances of the implication problem and several heuristics are derived that approximate this "lattice-exclusion" criterion in polynomial time. Finally, we provide experimental results that relate our work to results obtained from other existing inference algorithms.
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PDF链接：
https://arxiv.org/pdf/0810.5717