Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and conjunctive queries. Motivated by the increased theoretical and practical interest in navigational queries, this paper considers the question for which of these fragments decidability of querying extends to regular path queries (RPQs). In fact, decidability of RPQs has recently been shown to generally hold for the comprehensive family of all fragments that come with the guarantee of universal models being reasonably well-shaped (that is, being of finite cliquewidth). Yet, for the second major family of fragments, known as finite unification sets (short: fus), which are based on first-order-rewritability, corresponding results have been largely elusive so far. We complete the picture by showing that RPQ answering over arbitrary fus rulesets is undecidable. On the positive side, we establish that the problem is decidable for the prominent fus subclass of sticky rulesets, with the caveat that a very mild extension of the RPQ formalism turns the problem undecidable again.

翻译：本体查询应答领域的大量研究已识别出众多存在规则（亦称元组生成依赖）片段，这些片段在原子查询与合取查询的应答方面展现出可判定性。受导航查询理论与实际应用兴趣日益增长的驱动，本文探讨了这些片段中哪些能够将查询可判定性扩展至正则路径查询（RPQs）。事实上，近期研究已证明RPQs的可判定性普遍适用于所有保证通用模型具有良好形态（即具有有限团宽度）的片段族。然而，对于基于一阶可重写性的第二大类片段——有限统一集（简称fus），相应的研究成果迄今仍基本缺失。我们通过证明任意fus规则集上的RPQ应答是不可判定的，从而完善了这一研究图景。在积极方面，我们证实了该问题对于粘性规则集这一重要的fus子类是可判定的，但需注意：对RPQ形式体系进行极其温和的扩展将再次导致问题不可判定。