The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination analysis. It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given. But all-instance termination presents a challenge since the critical database and similar techniques do not work. In this paper, we develop a novel technique to characterize the activeness of all possible cycles of a certain length for the restricted chase, which leads to the formulation of a framework of parameterized classes of the finite restricted chase, called $k$-$\mathsf{safe}(\Phi)$ rule sets. This approach applies to any class of finite skolem chase identified with a condition of acyclicity. More generally, we show that the approach can be applied to the hierarchy of bounded rule sets previously only defined for the skolem chase. Experiments on a collection of ontologies from the web show the applicability of the proposed methods on real-world ontologies.

Requirement planning is one of the most critical tasks in the product development process. Despite its significant impact on the outcomes of the design process, engineering requirement planning is often conducted in an ad hoc manner without much structure. In particular, the requirement planning phase suffers from a lack of quantifiable measures for evaluating the quality of the generated requirements and also a lack of structure and formality in representing engineering requirements. The main objective of this research is to develop a formal Web Ontology Language ontology for standard representation of engineering requirements. The proposed ontology uses explicit semantics that makes the ontology amenable to automated reasoning. To demonstrate how the proposed ontology can support requirement analysis and evaluation in engineering design, three possible services enabled by the ontology are introduced in this paper. These services are information content measurement, specificity and completeness analysis, and requirement classification. The proposed ontology and its associated algorithms and tools are validated experimentally in this work.