Several types of dependencies have been proposed for the static analysis of
existential rule ontologies, promising insights about computational properties
and possible practical uses of a given set of rules, e.g., in ontology-based
query answering. Unfortunately, these dependencies are rarely implemented, so
their potential is hardly realised in practice. We focus on two kinds of rule
dependencies -- positive reliances and restraints -- and design and implement
optimised algorithms for their efficient computation. Experiments on real-world
ontologies of up to more than 100,000 rules show the scalability of our
approach, which lets us realise several previously proposed applications as
practical case studies. In particular, we can analyse to what extent rule-based
bottom-up approaches of reasoning can be guaranteed to yield redundancy-free
"lean" knowledge graphs (so-called cores) on practical ontologies.

通过针对存在规则本体的静态分析，研究了两种规则依赖性 - 正依赖性和约束性 - 并设计和实现了优化算法以实现其有效计算，从而分析了基于规则的自下而上的推理方法在现实本体上的可行性和实用性。实验证明了该方法的可扩展性，特别是在分析规则依赖性时，能产生不冗余的 “瘦” 知识图。