The disjunctive restricted chase is a sound and complete procedure for solving boolean conjunctive query entailment over knowledge bases of disjunctive existential rules. Alas, this procedure does not always terminate and checking if it does is undecidable. However, we can use acyclicity notions (sufficient conditions that imply termination) to effectively apply the chase in many real-world cases. To know if these conditions are as general as possible, we can use cyclicity notions (sufficient conditions that imply non-termination). In this paper, we discuss some issues with previously existing cyclicity notions, propose some novel notions for non-termination by dismantling the original idea, and empirically verify the generality of the new criteria.

翻译：析取式受限追踪是一种完备且正确的过程，用于判定涉及析取存在规则知识库上的布尔合取查询蕴涵问题。然而，该过程并非总是终止，且判定其是否终止属于不可判定问题。但我们可以利用无环性概念（保证终止的充分条件）在诸多实际场景中有效应用该追踪技术。为判断这些条件是否达到最大通用性，可借助循环性概念（保证非终止的充分条件）。本文探讨了既有循环性概念存在的若干问题，通过解构原始思想提出了新的非终止判定条件，并通过实验验证了新准则的通用性。