Polynomial Rewritings from Expressive Description Logics with Closed Predicates to Variants of Datalog

In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning about logic theories. Here we consider the setting of querying possibly incomplete data using logic theories, formalized as the evaluation of an ontology-mediated query (OMQ) that pairs a query with a theory, sometimes called an ontology, expressing background knowledge. This can be further enriched by specifying a set of closed predicates from the theory that are to be interpreted under the closed-world assumption, while the rest are interpreted with the open-world view. In this way we can retrieve more precise answers to queries by leveraging the partial completeness of the data. The central goal of this paper is to understand the relative expressiveness of OMQ languages in which the ontology is written in the expressive Description Logic (DL) ALCHOI and includes a set of closed predicates. We consider a restricted class of conjunctive queries. Our main result is to show that every query in this non-monotonic query language can be translated in polynomial time into Datalog with negation under the stable model semantics. To overcome the challenge that Datalog has no direct means to express the existential quantification present in ALCHOI, we define a two-player game that characterizes the satisfaction of the ontology, and design a Datalog query that can decide the existence of a winning strategy for the game. If there are no closed predicates, that is in the case of querying a plain ALCHOI knowledge base, our translation yields a positive disjunctive Datalog program of polynomial size. To the best of our knowledge, unlike previous translations for related fragments with expressive (non-Horn) DLs, these are the first polynomial time translations.

Managing Change in Graph-structured Data Using Description Logics (long version with appendix)

In this paper, we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from ensuring the satisfaction of a given set of integrity constraints after a given sequence of updates, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. We consider an action language in which actions are finite sequences of conditional insertions and deletions of nodes and labels, and use Description Logics for describing integrity constraints and (partial) states of the data. We then formalize the above data management problems as a static verification problem and several planning problems. We provide algorithms and tight complexity bounds for the formalized problems, both for an expressive DL and for a variant of DL-Lite.

Nested Regular Path Queries in Description Logics

Two-way regular path queries (2RPQs) have received increased attention recently due to their ability to relate pairs of objects by flexibly navigating graph-structured data. They are present in property paths in SPARQL 1.1, the new standard RDF query language, and in the XML query language XPath. In line with XPath, we consider the extension of 2RPQs with nesting, which allows one to require that objects along a path satisfy complex conditions, in turn expressed through (nested) 2RPQs. We study the computational complexity of answering nested 2RPQs and conjunctions thereof (CN2RPQs) in the presence of domain knowledge expressed in description logics (DLs). We establish tight complexity bounds in data and combined complexity for a variety of DLs, ranging from lightweight DLs (DL-Lite, EL) up to highly expressive ones. Interestingly, we are able to show that adding nesting to (C)2RPQs does not affect worst-case data complexity of query answering for any of the considered DLs. However, in the case of lightweight DLs, adding nesting to 2RPQs leads to a surprising jump in combined complexity, from P-complete to Exp-complete.

Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations.