Abstract
Recent years have witnessed the successful application of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. However, it is not yet well-understood to what extent ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a general framework based on a view of relations as regions, which allows us to study the compatibility between ontological knowledge and different types of vector space embeddings. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding methods are not capable of modelling even very simple types of rules, which in particular also means that they are not able to learn the type of dependencies captured by such rules. Second, we study a model in which relations are modelled as convex regions. We show particular that ontologies which are expressed using so-called quasi-chained existential rules can be exactly represented using convex regions, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.
Abstract (translated)
近年来见证了知识图的低维向量空间表示的成功应用，以预测遗漏的事实或发现错误的事实。然而，尚未充分理解本体论知识的程度，例如：作为一组（存在的）规则给出，可以以原则方式嵌入。为了解决这个缺点，在本文中，我们引入了一个基于关系视图作为区域的一般框架，这使我们能够研究本体知识与不同类型的向量空间嵌入之间的兼容性。我们的技术贡献是双重的。首先，我们展示了一些最流行的现有嵌入方法甚至不能对非常简单的规则类型进行建模，这尤其也意味着它们无法学习这些规则捕获的依赖关系的类型。其次，我们研究了一种模型，其中关系被建模为凸区域。我们特别指出，使用所谓的准链式存在性规则表达的本体可以使用凸区域精确表示，使得使用该向量空间嵌入引起的任何事实集合在逻辑上是一致的并且相对于输入是演绎地闭合的。本体论。
URL
https://arxiv.org/abs/1805.10461
