Finite query answering in expressive description logics with transitive roles

We study the problem of finite ontology mediated query an-swering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA isrelevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challenging: FOMQA is undecidable for SHOIF and only known to be decidable for the Horn fragment of ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI, SOF, and SIF. Our approach is to characterise models relevant for deciding finite query entailment. Relying on a certain regularity of these models, we develop automata-based decision procedures with optimal complexity bounds

Conjunctive Query Answering for the Description Logic SHIQ

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP

Combined FO rewritability for conjunctive query answering in DL-Lite

Standard description logic (DL) reasoning services such as satisfiability and subsumption mainly aim to support TBox design. When the design stage is over and the TBox is used in an actual application, it is usually combined with instance data stored in an ABox, and therefore query answering becomes the most importan

Querying the Unary Negation Fragment with Regular Path Expressions

The unary negation fragment of first-order logic (UNFO) has recently been proposed as a generalization of modal logic that shares many of its good computational and model-theoretic properties. It is attractive from the perspective of database theory because it can express conjunctive queries (CQs) and ontologies formulated in many description logics (DLs). Both are relevant for ontology-mediated querying and, in fact, CQ evaluation under UNFO ontologies (and thus also under DL ontologies) can be `expressed\u27 in UNFO as a satisfiability problem. In this paper, we consider the natural extension of UNFO with regular expressions on binary relations. The resulting logic UNFOreg can express (unions of) conjunctive two-way regular path queries (C2RPQs) and ontologies formulated in DLs that include transitive roles and regular expressions on roles. Our main results are that evaluating C2RPQs under UNFOreg ontologies is decidable, 2ExpTime-complete in combined complexity, and coNP-complete in data complexity, and that satisfiability in UNFOreg is 2ExpTime-complete, thus not harder than in UNFO

Finite Satisfiability of Unary Negation Fragment with Transitivity

We show that the finite satisfiability problem for the unary negation fragment with an arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require that some binary symbols are interpreted as arbitrary transitive relations, some as partial orders and some as equivalences. We also consider finite satisfiability of various extensions of our primary logic, in particular capturing the concepts of nominals and role hierarchies known from description logic. As the unary negation fragment can express unions of conjunctive queries, our results have interesting implications for the problem of finite query answering, both in the classical scenario and in the description logics setting

Temporal Conjunctive Queries in Expressive DLs with Non-simple Roles

In Ontology-Based Data Access (OBDA), user queries are evaluated over a set of facts under the open world assumption, while taking into account background knowledge given in the form of a Description Logic (DL) ontology. Motivated by situation awareness applications, temporal conjunctive queries (TCQs) have recently been proposed as a useful extension of traditional OBDA to support the processing of temporal information. This paper extends the existing complexity analysis of TCQ entailment to very expressive DLs underlying the OWL 2 standard, and in contrast to previous work also allows for queries containing transitive roles.This is an extended version of the paper “Temporal Conjunctive Queries in Expressive Description Logics with Transitive Roles”, published in the Proceedings of the 28th Australasian Joint Conference on Artificial Intelligence (AI’15)