Revisiting Chase Termination for Existential Rules and their Extension to Nonmonotonic Negation
This work addresses a foundational issue in ontology-based data access, offering incremental improvements to termination conditions for existential rules.
The paper tackles the problem of ensuring termination for the chase algorithm in existential rules, proposing a new tool to extend existing acyclicity conditions while maintaining good complexity properties, and extends these results to rules with nonmonotonic negation under stable model semantics.
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. Several variants of the chase have been proposed. In the first part of this paper, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. In the second part, we study the extension to existential rules with nonmonotonic negation under stable model semantics, discuss the relevancy of the chase variants for these rules and further extend acyclicity results obtained in the positive case.