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

Adding DL-Lite TBoxes to Proper Knowledge Bases

Levesque’s proper knowledge bases (proper KBs) correspond to infinite sets of ground positive and negative facts, with the notable property that for FOL formulas in a certain normal form, which includes conjunctive queries and positive queries possibly extended with a controlled form of negation, entailment reduces to formula evaluation. However proper KBs represent extensional knowledge only. In description logic terms, they correspond to ABoxes. In this paper, we augment them with DL-Lite TBoxes, expressing intensional knowledge (i.e., the ontology of the domain). DL-Lite has the notable property that conjunctive query answering over TBoxes and standard description logic ABoxes is re- ducible to formula evaluation over the ABox only. Here, we investigate whether such a property extends to ABoxes consisting of proper KBs. Specifically, we consider two DL-Lite variants: DL-Literdfs , roughly corresponding to RDFS, and DL-Lite_core , roughly corresponding to OWL 2 QL. We show that when a DL- Lite_rdfs TBox is coupled with a proper KB, the TBox can be compiled away, reducing query answering to evaluation on the proper KB alone. But this reduction is no longer possible when we associate proper KBs with DL-Lite_core TBoxes. Indeed, we show that in the latter case, query answering even for conjunctive queries becomes coNP-hard in data complexity

Ontology-based data access with databases: a short course

Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop

Unions of conjunctive queries in SHOQ

Conjunctive queries play an important role as an expressive query language in Description Logics (DLs). Decision procedures for expressive Description Logics are, however, only recently emerging and it is still an open question whether answering conjunctive queries is decidable for the DL SHOIQ that underlies the OWL DL standard. In fact, no decision procedure was known for expressive DLs that contain nominals. In this paper, we close this gap by providing a decision procedure for entailment of unions of conjunctive queries in SHOQ. Our algorithm runs in deterministic time single exponential in the size of the knowledge base and double exponential in the size of the query, which is the same as for SHIQ. Our procedure also shows that SHOQ knowledge base consistency is indeed ExpTime-complete, which was, to the best of our knowledge, always conjectured but never proved