Abstract Independence relations in general include exponentially many statements of independence, that is, exponential in the number of variables involved. These relations are typically characterised however, by a small set of such statements and an associated set of derivation rules. While various computational problems on independence relations can be solved by manipulating these smaller sets without the need to explicitly generate the full relation, existing algorithms for constructing these sets are associated with often prohibitively high running times. In this paper, we introduce a lattice structure for organising sets of independence statements and show that current algorithms are rendered computationally less demanding by exploiting new insights in the structural properties of independence gained from this lattice organisation. By means of a range of experimental results, we subsequently demonstrate that through the lattice organisation indeed a substantial gain in efficiency is achieved for fast-closure computation of semi-graphoid independence relations in practice.

中文翻译：

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用于高效闭包计算的基于格的独立关系表示

摘要 独立关系一般包括指数级的许多独立性陈述，即涉及的变量数量呈指数级增长。然而，这些关系的典型特征是一小组这样的陈述和一组相关的推导规则。虽然可以通过操作这些较小的集合来解决独立关系的各种计算问题，而无需显式生成完整的关系，但用于构建这些集合的现有算法通常与高得令人望而却步的运行时间相关联。在本文中，我们介绍了一种用于组织独立性陈述集的格结构，并表明通过利用从这种格组织中获得的独立性结构特性的新见解，当前算法在计算上的要求较低。