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Queries with Negation and Inequalities over Lightweight Ontologies

28 Pages Posted: 9 Jul 2018 First Look: Accepted

See all articles by Victor Gutierrez-Basulto

Victor Gutierrez-Basulto

University of Bremen - Department of Mathematics and Computer Science

Yazmin Ibanez-Garcia

University of Bremen - Department of Mathematics and Computer Science; Free University of Bozen-Bolzano - KRDB Research Centre

Roman Kontchakov

University of London - Department of Computer Science & Information Systems

Egor V. Kostylev

University of Oxford; University of Edinburgh

Abstract

While the problem of answering positive existential queries, in particular, conjunctive queries (CQs) and unions of CQs, over description logic ontologies has been studied extensively, there have been few attempts to analyse queries with negated atoms. Our aim is to sharpen the complexity landscape of the problem of answering CQs with negation and inequalities in lightweight description logics of the DL-Lite and &1 families. We begin by considering queries with safe negation and show that there is a surprisingly significant increase in the complexity from AC0 to undecidability (even if the ontology and query are fixed and only the data is regarded as input). We also investigate the problem of answering queries with inequalities and show that answering a single CQ with one inequality over DL-Lite with role inclusions is undecidable. In the light of our undecidability results, we explore syntactic restrictions to attain efficient query answering with negated atoms. In particular, we identify a novel class of local CQs with inequalities, for which query answering over DL-Lite is decidable.

Keywords: description logics, ontological query answering, conjunctive queries with negation, inequalities, DL-Lite, EL

Suggested Citation

Gutierrez-Basulto, Victor and Ibanez-Garcia, Yazmin and Kontchakov, Roman and Kostylev, Egor V., Queries with Negation and Inequalities over Lightweight Ontologies (2015). Journal of Web Semantics First Look. Available at SSRN: https://ssrn.com/abstract=3199213 or http://dx.doi.org/10.2139/ssrn.3199213

Victor Gutierrez-Basulto

University of Bremen - Department of Mathematics and Computer Science ( email )

Germany

Yazmin Ibanez-Garcia

University of Bremen - Department of Mathematics and Computer Science ( email )

Germany

Free University of Bozen-Bolzano - KRDB Research Centre ( email )

Italy

Roman Kontchakov (Contact Author)

University of London - Department of Computer Science & Information Systems ( email )

Malet Street, Bloomsbury
London
United Kingdom

Egor V. Kostylev

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Edinburgh

Old College
South Bridge
Edinburgh, Scotland EH8 9JY
United Kingdom

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