The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Query Rewriting in DL-Lite ( HN ) horn Elena Botoeva, Alessandro Artale, and Diego Calvanese KRDB Research Centre Free University of Bozen-Bolzano I-39100 Bolzano, Italy Description Logics Workshop, 2010 Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 1/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Outline 1 Motivation 2 The DL DL - Lite ( HN ) horn 3 Knowledge Base Satisfiability 4 Query Answering 5 Conclusions Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 2/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Motivation: Ontology-Based Data Access Application Application 1 Application 2 response response query query Data Data Data source 1 source 2 source 3 Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 3/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Motivation: Ontology-Based Data Access • Ontologies are used for accessing data Application Application query response Ontology Ontology C 1 C 1 R 1 R 1 C 3 C 3 A 1 A 1 A 2 A 2 C 2 C 2 Data Data Data source 1 source 2 source 3 • An ontology provides a high-level conceptual view of information sources • Data sources can be queried through ontologies Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 3/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Query Answering by Rewriting • We want to compute certain answers to a query Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 4/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Query Answering by Rewriting • We want to compute certain answers to a query • Rewriting approach: 1 Rewrite the query using the constraints in the ontology 2 Evaluate the rewritten query over the database Reasoning Reasoning Schema / Query Result Ontology Logical Rewritten Schema Query Data Source Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 4/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Query Answering by Rewriting: Example Ontology: O = { PhDStudent ⊑ Student } Database: DB A = { PhDStudent (john) } Query: q ( x ) ← Student ( x ) Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 5/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Query Answering by Rewriting: Example Ontology: O = { PhDStudent ⊑ Student } Database: DB A = { PhDStudent (john) } Query: q ( x ) ← Student ( x ) • The rewriting of q : q ucq ( x ) ← Student ( x ) q ucq ( x ) ← PhDStudent ( x ) • By evaluating the rewriting over the ABox viewed as a DB : eval ( q ucq , DB A ) = { john } = ans ( q , �O , DB A � ) Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 5/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn FOL Rewritable Logics • Such a rewriting approach can be applied only to FOL rewritable logics. Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 6/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn FOL Rewritable Logics • Such a rewriting approach can be applied only to FOL rewritable logics. • DL-Lite is a family of logics that has been shown to enjoy FOL rewritability: ◮ DL-Lite R , DL-Lite F , DL-Lite A Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 6/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn FOL Rewritable Logics • Such a rewriting approach can be applied only to FOL rewritable logics. • DL-Lite is a family of logics that has been shown to enjoy FOL rewritability: ◮ DL-Lite R , DL-Lite F , DL-Lite A • Extended DL-Lite family: additional constructs have been proposed ◮ DL-Lite ( HN ) is the most interesting logic horn Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 6/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Outline 1 Motivation 2 The DL DL - Lite ( HN ) horn 3 Knowledge Base Satisfiability 4 Query Answering 5 Conclusions Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 7/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn In this work we consider the logic DL-Lite ( HN ) : horn • The most expressive tractable variant of DL-Lite [ACKZ09]. Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 8/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn In this work we consider the logic DL-Lite ( HN ) : horn • The most expressive tractable variant of DL-Lite [ACKZ09]. • Extends DL-Lite with Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 8/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn In this work we consider the logic DL-Lite ( HN ) : horn • The most expressive tractable variant of DL-Lite [ACKZ09]. • Extends DL-Lite with ◮ role inclusions H • hasConfPaper ⊑ hasPublication Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 8/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn In this work we consider the logic DL-Lite ( HN ) : horn • The most expressive tractable variant of DL-Lite [ACKZ09]. • Extends DL-Lite with ◮ role inclusions H • hasConfPaper ⊑ hasPublication ◮ number restrictions N • PhDStudent ⊑ ≥ 2 hasConfPaper • ≥ 2 teaches − ⊑ ⊥ Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 8/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn In this work we consider the logic DL-Lite ( HN ) : horn • The most expressive tractable variant of DL-Lite [ACKZ09]. • Extends DL-Lite with ◮ role inclusions H • hasConfPaper ⊑ hasPublication ◮ number restrictions N • PhDStudent ⊑ ≥ 2 hasConfPaper • ≥ 2 teaches − ⊑ ⊥ ◮ horn inclusions horn • Student ⊓ ≥ 1 teaches ⊑ PhDStudent Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 8/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn Questions Addressed by Our Work For the logic DL-Lite ( HN ) horn : • Can we check ontology satisfiability by relying on RDB technology? • Can we answer queries by relying on RDB technology? • Can we extend the practical algorithms developed for the simpler DL-Lite logics? • What is the complexity of such algorithms? Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 9/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn : Syntax Concept and role expressions B ::= ⊥ | A | ≥ k R R ::= P | P − TBox assertions B 1 ⊓ · · · ⊓ B n ⊑ B R 1 ⊑ R 2 Dis( R 1 , R 2 ) Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 10/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn DL-Lite ( HN ) horn : Syntax Concept and role expressions B ::= ⊥ | A | ≥ k R R ::= P | P − TBox assertions B 1 ⊓ · · · ⊓ B n ⊑ B R 1 ⊑ R 2 Dis( R 1 , R 2 ) Restriction to ensure FOL rewritability: if R has a proper sub-role, then ≥ k R with k ≥ 2 does not occur in the lhs of concept inclusions. Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 10/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn A DL-Lite ( HN ) TBox horn • basic concept inclusion ≥ 1 hasPublication − ⊑ Publication Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 11/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn A DL-Lite ( HN ) TBox horn • basic concept inclusion ≥ 1 hasPublication − ⊑ Publication • role inclusion hasConfPaper ⊑ hasPublication Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 11/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn A DL-Lite ( HN ) TBox horn • basic concept inclusion ≥ 1 hasPublication − ⊑ Publication • role inclusion hasConfPaper ⊑ hasPublication • number restrictions PhDStudent ⊑ ≥ 2 hasConfPaper Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 11/25 horn
The DL DL - Lite ( HN ) Motivation Knowledge Base Satisfiability Query Answering Conclusions horn A DL-Lite ( HN ) TBox horn • basic concept inclusion ≥ 1 hasPublication − ⊑ Publication • role inclusion hasConfPaper ⊑ hasPublication • number restrictions PhDStudent ⊑ ≥ 2 hasConfPaper • horn inclusion Student ⊓ ≥ 1 teaches ⊑ PhDStudent Query Rewriting in DL-Lite ( HN ) Botoeva, Artale, Calvanese 11/25 horn
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