Parallelisable Existential Rules: a Story of Pieces
This work addresses the challenge of efficient reasoning in ontology-based data integration for knowledge representation, providing incremental theoretical insights into rule set properties.
The paper tackles the problem of characterizing parallelisable sets of existential rules, which allow the chase reasoning process to be computed in a single breadth-first step from any database instance. It shows that parallelisable rule sets are exactly those that are both bounded for the chase and belong to a novel class called pieceful, which includes frontier-guarded existential rules and datalog.
In this paper, we consider existential rules, an expressive formalism well suited to the representation of ontological knowledge and data-to-ontology mappings in the context of ontology-based data integration. The chase is a fundamental tool to do reasoning with existential rules as it computes all the facts entailed by the rules from a database instance. We introduce parallelisable sets of existential rules, for which the chase can be computed in a single breadth-first step from any instance. The question we investigate is the characterization of such rule sets. We show that parallelisable rule sets are exactly those rule sets both bounded for the chase and belonging to a novel class of rules, called pieceful. The pieceful class includes in particular frontier-guarded existential rules and (plain) datalog. We also give another characterization of parallelisable rule sets in terms of rule composition based on rewriting.