Full hierarchical dependencies (FHDs) constitute a large class of relational dependencies. A relation exhibits an FHD precisely when it can be decomposed into at least two of its projections without loss of information. Therefore, FHDs generalise multivalued dependencies (MVDs) in which case the number of these projections is precisely two. The implication of FHDs has been defined in the context of some fixed finite universe.
This paper identifies a sound and complete set of inference rules for the implication of FHDs. This ax-iomatisation is very reminiscent of that for MVDs. Then, an alternative notion of FHD implication is introduced in which the underlying set of attributes is left undetermined. The main result proposes a finite axiomatisation for FHD implication in undetermined universes. Moreover, the result clarifies the role of the complementation rule as a mere means of database normalisation. In fact, an axiomatisation for FHD implication in fixed universes is proposed which allows to infer any FHDs either without using the complementation rule at all or only in the very last step of the inference. This also characterises the expressiveness of an incomplete set of inference rules in fixed universes. The results extend previous work on MVDs by Biskup.
完整的层次依赖关系(FHD)构成了一大类关系依赖关系。当一个关系可以分解为至少至少 I>个投影而又不丢失信息时,它就显示出FHD。因此,FHD概括了多值依赖关系(MVD),在这种情况下,这些投影的数量恰好是两个。 FHD的含义是在某些固定的有限宇宙的背景下定义的。 P>
本文为FHD的含义确定了一套完善的推理规则。这种轴心化非常类似于MVD。然后,引入了FHD蕴涵的替代概念,其中未确定基础属性集。主要结果提出了在不确定的宇宙中对FHD表示的有限公理化。此外,结果阐明了补充规则作为数据库规范化手段的作用。实际上,提出了固定宇宙中FHD涵义的公理化,它允许完全不使用补充规则或仅在推理的最后一步来推断任何FHD。这也表征了固定宇宙中不完整的推理规则集的表达性。该结果扩展了Biskup先前关于MVD的工作。 P>
机译:概率推理:任务相依性和概率加权的个体差异通过分层贝叶斯建模揭示
机译:海地刘等人的依赖距离,分层结构和单词命中评论的分配距离,层次结构和单词命中评论。
机译:通过分层聚类提供了亲属和Sibship推断的高效推断
机译:关于完整分层依赖性的推论
机译:依赖网络中的快速推理算法。
机译:概率推论:分层贝叶斯模型揭示了任务相关性和概率加权的个体差异
机译:概率推论:分层贝叶斯模型揭示了任务相关性和概率加权的个体差异