Answering Path Queries under Linear and Guarded Existential Rules
Provides a complete complexity picture for navigational query answering under guarded existential rules, extending known results for conjunctive queries.
This paper studies the complexity of answering two-way (conjunctive) regular path queries over knowledge bases with guarded existential rules. It shows that for linear rules, data complexity is NL-complete, matching plain graph databases, while combined complexity ranges from PTime to ExpTime depending on arity; for guarded rules, complexity matches that of conjunctive queries: 2ExpTime-complete combined (ExpTime with bounded arity) and PTime data.
Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries (CQs), navigational queries have gained increasing attention. In this paper, we investigate the complexity of answering two-way (conjunctive) regular path queries ((C)RPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that (C)RPQ answering is NL-complete in data complexity, which matches the data complexity of answering RPQs over plain graph databases (i.e., without an ontology). In combined complexity, both tasks are ExpTime-complete in the general case, but RPQ and CRPQ answering drop to PTime-complete and PSpace-complete respectively if there is a bound on predicate arity. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of (C)RPQ answering is the same as for CQs, namely 2ExpTime-complete in combined complexity (ExpTime-complete in the bounded-arity case) and PTime-complete in data complexity.