We study the notion of boundedness in the context of positive existential rules, that is, whether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance. By focussing our attention on the oblivious and the semi-oblivious chase variants, we give a characterization of boundedness in terms of FO-rewritability and chase termination. We show that it is decidable to recognize if a set of rules is bounded for several classes and outline the complexity of the problem. This report contains the paper published at IJCAI 2019 and an appendix with full proofs.

中文翻译：

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存在规则的不经意和半不经意的有界

我们在肯定存在规则的背景下研究有界性的概念，即是否存在与初始实例无关的追逐程序深度的上限。通过将注意力集中在不经意和半不经意的追踪变体上，我们在 FO 可重写性和追踪终止方面给出了有界性的特征。我们表明，识别一组规则是否适用于多个类并概述问题的复杂性是可判定的。本报告包含在 IJCAI 2019 上发表的论文和带有完整证明的附录。