Complexity of Answering Counting Aggregate Queries over DL-Lite

Abstract The ontology based data access model assumes that users access data by means of an ontology, which is often described in terms of description logics. As a consequence, languages for managing ontologies now need algorithms not only to decide standard reasoning problems, but also to answer database-like queries. However, fundamental database aggregate queries, such as the ones using functions COUNT and COUNT DISTINCT, have received very little attention in this context, and even defining appropriate semantics for their answers over ontologies appears to be a non-trivial task. Our goal is to study the problem of answering database queries with aggregation in the context of ontologies. This paper presents an intuitive semantics for answering counting queries, followed by a comparison with similar approaches that have been taken in different database contexts. Afterwards, it exhibits a thorough study of the computational complexity of evaluating counting queries conforming to this semantics. Our results show that answering such queries over ontologies is decidable, but generally intractable. However, our semantics promotes awareness on the information that can be obtained by querying ontologies and raises the need to look for suitable approximations or heuristics in order to allow efficient evaluation of this widely used class of queries.

[1]  Xin He,et al.  Scalar aggregation in inconsistent databases , 2003, Theor. Comput. Sci..

[2]  Roman Kontchakov,et al.  An Update on Query Answering with Restricted Forms of Negation , 2012, RR.

[3]  Phokion G. Kolaitis,et al.  Answering aggregate queries in data exchange , 2008, PODS.

[4]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[5]  Diego Calvanese,et al.  The MASTRO system for ontology-based data access , 2011, Semantic Web.

[6]  Leonid Libkin,et al.  Data exchange and incomplete information , 2006, PODS '06.

[7]  Werner Nutt,et al.  Deciding equivalences among conjunctive aggregate queries , 2007, JACM.

[8]  Carsten Lutz,et al.  The Combined Approach to Ontology-Based Data Access , 2011, IJCAI.

[9]  Marcelo Arenas,et al.  Query Languages for Data Exchange: Beyond Unions of Conjunctive Queries , 2009, ICDT '09.

[10]  Egor V. Kostylev,et al.  Answering Counting Aggregate Queries over Ontologies of the DL-Lite Family , 2013, AAAI.

[11]  Riccardo Rosati,et al.  The Limits of Querying Ontologies , 2007, ICDT.

[12]  Magdalena Ortiz,et al.  Conjunctive Regular Path Queries in Lightweight Description Logics , 2013, IJCAI.

[13]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[14]  Raghu Ramakrishnan,et al.  Database Management Systems , 1976 .

[15]  Boris Motik,et al.  OWL 2: The next step for OWL , 2008, J. Web Semant..

[16]  Diego Calvanese,et al.  Aggregate queries over ontologies , 2008, ONISW '08.

[17]  Diego Calvanese,et al.  The DL-Lite Family and Relations , 2009, J. Artif. Intell. Res..

[18]  Franz Baader,et al.  Description Logics with Aggregates and Concrete Domains , 1997, Description Logics.

[19]  Egor V. Kostylev,et al.  Conjunctive Queries with Negation over DL-Lite: A Closer Look , 2013, RR.

[20]  Bogdan Kostov,et al.  Count Aggregation in Semantic Queries , 2013, SSWS@ISWC.

[21]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[22]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[23]  Diego Calvanese,et al.  Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family , 2007, Journal of Automated Reasoning.

[24]  Magdalena Ortiz,et al.  Answering Expressive Path Queries over Lightweight DL Knowledge Bases , 2012, Description Logics.

[25]  Egor V. Kostylev,et al.  XPath for DL Ontologies , 2015, AAAI.

[26]  Yuri Gurevich,et al.  The Classical Decision Problem , 1997, Perspectives in Mathematical Logic.