Checking Chase Termination over Ontologies of Existential Rules with Equality

The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality. To enable its effective use, we can apply acyclicity notions; that is, sufficient conditions that guarantee chase termination. Unfortunately, most of these notions have only been defined for existential rule sets without equality. A proposed solution to circumvent this issue is to treat equality as an ordinary predicate with an explicit axiomatisation. We empirically show that this solution is not efficient in practice and propose an alternative approach. More precisely, we show that, if the chase terminates for any equality axiomatisation of an ontology, then it terminates for the original ontology (which may contain equality). Therefore, one can apply existing acyclicity notions to check chase termination over an axiomatisation of an ontology and then use the original ontology for reasoning. We show that, in practice, doing so results in a more efficient reasoning procedure. Furthermore, we present equality model-faithful acyclicity, a general acyclicity notion that can be directly applied to ontologies with equality

Revisiting Chase Termination for Existential Rules and their Extension to Nonmonotonic Negation

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.Comment: This paper appears in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Goal-Driven Query Answering for Existential Rules with Equality

Inspired by the magic sets for Datalog, we present a novel goal-driven approach for answering queries over terminating existential rules with equality (aka TGDs and EGDs). Our technique improves the performance of query answering by pruning the consequences that are not relevant for the query. This is challenging in our setting because equalities can potentially affect all predicates in a dataset. We address this problem by combining the existing singularization technique with two new ingredients: an algorithm for identifying the rules relevant to a query and a new magic sets algorithm. We show empirically that our technique can significantly improve the performance of query answering, and that it can mean the difference between answering a query in a few seconds or not being able to process the query at all

Query Rewriting and Optimization for Ontological Databases

Ontological queries are evaluated against a knowledge base consisting of an extensional database and an ontology (i.e., a set of logical assertions and constraints which derive new intensional knowledge from the extensional database), rather than directly on the extensional database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper, we discuss two important aspects of this problem: query rewriting and query optimization. Query rewriting consists of the compilation of an ontological query into an equivalent first-order query against the underlying extensional database. We present a novel query rewriting algorithm for rather general types of ontological constraints which is well-suited for practical implementations. In particular, we show how a conjunctive query against a knowledge base, expressed using linear and sticky existential rules, that is, members of the recently introduced Datalog+/- family of ontology languages, can be compiled into a union of conjunctive queries (UCQ) against the underlying database. Ontological query optimization, in this context, attempts to improve this rewriting process so to produce possibly small and cost-effective UCQ rewritings for an input query.Comment: arXiv admin note: text overlap with arXiv:1312.5914 by other author

Computing FO-Rewritings in EL in Practice: from Atomic to Conjunctive Queries

A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the description logic EL and the actual query is a conjunctive query and show that rewritings of such OMQs can be efficiently computed in practice, in a sound and complete way. Our approach combines a reduction with a decomposed backwards chaining algorithm for OMQs that are based on the simpler atomic queries, also illuminating the relationship between first-order rewritings of OMQs based on conjunctive and on atomic queries. Experiments with real-world ontologies show promising results

Datalog rewriting for Guarded TGDs

We deal with the problem of fact entailment with respect to a database and a set of integrity constraints, focusing on the case of Guarded tuple-generating dependencies (GTGDs). The original approach to the problem in the literature is via forward reasoning or "chasing", where one completes the input database by adding fresh elements and facts. This completion process may be infinite, but in the case of GTGDs it is known that one can compute a point where the chase can be cut off without missing any base facts. Another approach is by forming an automaton and checking it for emptiness. Neither of these approaches scales to large input datasets. An alternative approach is to rewrite the constraints into Datalog: the Datalog rewriting can be generated in advance of any dataset and will produce the same base facts as the original constraints. It is known that Datalog rewritings always exist. But to our knowledge the approach has never been implemented. In this work we overview effective algorithms to Datalog rewriting of GTGDs. This presents work that will appear in VLDB 2022