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48
Data complexity of query answering in description logics
 IN PROC. OF KR 2006
, 2006
"... In this paper we study data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by an ABox and a TBox. In particular, we are interested in characterizing the FOLreducibility and the polynomial tractability boundaries of conjunctive query answering, dependi ..."
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Cited by 210 (75 self)
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In this paper we study data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by an ABox and a TBox. In particular, we are interested in characterizing the FOLreducibility and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the Description Logic used to specify the knowledge base. FOLreducibility means that query answering can be reduced to evaluating queries over the database corresponding to the ABox. Since firstorder queries can be expressed in SQL, the importance of FOLreducibility is that, when query answering enjoys this property, we can take advantage of Data Base Management System (DBMS) techniques for both representing data, i.e., ABox assertions, and answering queries via reformulation into SQL. What emerges from our complexity analysis is that the Description Logics of the DLLite family are the maximal logics allowing conjunctive query answering through standard database technology. In this sense, they are the first Description Logics specifically tailored for effective query answering over very large ABoxes.
Querying the guarded fragment
 PROCEEDINGS OF THE 25TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS 2010
, 2010
"... Evaluating a Boolean conjunctive query q against a guarded firstorder theory ϕ is equivalent to checking whether ϕ ∧ ¬q is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity ..."
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Cited by 36 (12 self)
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Evaluating a Boolean conjunctive query q against a guarded firstorder theory ϕ is equivalent to checking whether ϕ ∧ ¬q is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity, and finitemodel property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati’s finite chase, we prove for guarded theories ϕ and (unions of) conjunctive queries q that (i) ϕ  = q iff ϕ =fin q, that is, iff q is true in each finite model of ϕ and (ii) determining whether ϕ  = q is 2EXPTIMEcomplete. We further show the following results: (iii) the existence of polynomialsize conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the cliqueguarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomialtime solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded bisimulation invariant PTIME.
Query Answering in the Horn Fragments of the Description Logics SHOIQ and SROIQ
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... The high computational complexity of the expressive Description Logics (DLs) that underlie the OWL standard has motivated the study of their Horn fragments, which are usually tractable in data complexity and can also have lower combined complexity, particularly for query answering. In this paper we ..."
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Cited by 19 (8 self)
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The high computational complexity of the expressive Description Logics (DLs) that underlie the OWL standard has motivated the study of their Horn fragments, which are usually tractable in data complexity and can also have lower combined complexity, particularly for query answering. In this paper we provide algorithms for answering conjunctive 2way regular path queries (2CRPQs), a nontrivial generalization of plain conjunctive queries, in the Horn fragments of the DLs SHOIQ and SROIQ underlying OWL 1 and OWL 2. We show that the combined complexity of the problem is ExpTimecomplete for HornSHOIQ and 2ExpTimecomplete for the more expressive HornSROIQ, butisPTimecomplete in data complexity for both. In contrast, even decidability of plain conjunctive queries is still open for full SHOIQ and SROIQ. These are the first completeness results for query answering in DLs with inverses, nominals, and counting, and show that for the considered logics the problem is not more expensive than standard reasoning.
On (In)Tractability of OBDA with OWL 2 QL
"... Abstract. We show that, although conjunctive queries over OWL 2 QL ontologies are reducible to database queries, no algorithm can construct such a reduction in polynomial time without changing the data. On the other hand, we give a polynomial reduction for OWL 2 QL ontologies without role inclusions ..."
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Cited by 17 (7 self)
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Abstract. We show that, although conjunctive queries over OWL 2 QL ontologies are reducible to database queries, no algorithm can construct such a reduction in polynomial time without changing the data. On the other hand, we give a polynomial reduction for OWL 2 QL ontologies without role inclusions. 1
Temporalizing ontologybased data access
 In Proc. CADE24, LNCS 7898
, 2013
"... Abstract. Ontologybased data access (OBDA) generalizes query answering in databases towards deduction since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrai ..."
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Cited by 15 (5 self)
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Abstract. Ontologybased data access (OBDA) generalizes query answering in databases towards deduction since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As query language we consider an extension of the wellknown propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as ontology language we use the prototypical expressive DL ALC. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem. 1
Query Answering in Description Logics with Transitive Roles
, 2009
"... We study the computational complexity of conjunctive query answering w.r.t. ontologies formulated in fragments of the description logic SHIQ. Our main result is the identification of two new sources of complexity: the combination of transitive roles and role hierarchies which results in 2EXPTIMEhar ..."
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Cited by 14 (7 self)
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We study the computational complexity of conjunctive query answering w.r.t. ontologies formulated in fragments of the description logic SHIQ. Our main result is the identification of two new sources of complexity: the combination of transitive roles and role hierarchies which results in 2EXPTIMEhardness, and transitive roles alone which result in CONEXPTIMEhardness. These bounds complement the existing result that inverse roles make query answering in SHIQ 2EXPTIMEhard. We also show that conjunctive query answering with transitive roles, but without inverse roles and role hierarchies, remains in EXPTIME if the ABox is treeshaped.
V.: Temporal query answering in the description logic DLLite
 In: Proc. of the 9th Int. Symposium on Frontiers of Combining Systems (FroCoS’13). LNCS
, 2013
"... Abstract. Ontologybased data access (OBDA) generalizes query answering in relational databases. It allows to query a database by using the language of an ontology, abstracting from the actual relations of the database. For ontologies formulated in Description Logics of the DLLite family, OBDA can ..."
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Cited by 13 (4 self)
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Abstract. Ontologybased data access (OBDA) generalizes query answering in relational databases. It allows to query a database by using the language of an ontology, abstracting from the actual relations of the database. For ontologies formulated in Description Logics of the DLLite family, OBDA can be realized by rewriting the query into a classical firstorder query, e.g. an SQL query, by compiling the information of the ontology into the query. The query is then answered using classical database techniques. In this paper, we consider a temporal version of OBDA. We propose a temporal query language that combines a linear temporal logic with queries over DLLitecoreontologies. This language is wellsuited to express temporal properties of dynamical systems and is useful in contextaware applications that need to detect specific situations. Using a firstorder rewriting approach, we transform our temporal queries into queries over a temporal database. We then present three approaches to answering the resulting queries, all having different advantages and drawbacks. 1
Tractable Queries for Lightweight Description Logics
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... It is a classic result in database theory that conjunctive query (CQ) answering, which is NPcomplete in general, is feasible in polynomial time when restricted to acyclic queries. Subsequent results identified more general structural properties of CQs (like bounded treewidth) which ensure tractable ..."
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Cited by 12 (4 self)
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It is a classic result in database theory that conjunctive query (CQ) answering, which is NPcomplete in general, is feasible in polynomial time when restricted to acyclic queries. Subsequent results identified more general structural properties of CQs (like bounded treewidth) which ensure tractable query evaluation. In this paper, we lift these tractability results to knowledge bases formulated in the lightweight description logics DLLite and ELH. The proof exploits known properties of query matches in these logics and involves a querydependent modification of the data. To obtain a more practical approach, we propose a concrete polynomialtime algorithm for answering acyclic CQs based on rewriting queries into datalog programs. A preliminary evaluation suggests the interest of our approach for handling large acyclic CQs.
Unary negation
, 2011
"... We study fragments of firstorder logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the µcalculus, as well as conjunctive queries and monadic ..."
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Cited by 12 (4 self)
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We study fragments of firstorder logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and the µcalculus, as well as conjunctive queries and monadic Datalog. We show that satisfiability and finite satisfiability are decidable for both fragments, and we pinpoint the complexity of satisfiability, finite satisfiability, and model checking. We also show that the unary negation fragment of firstorder logic is modeltheoretically very well behaved. In particular, it enjoys Craig interpolation and the Beth property.
Towards a unifying approach to representing and querying temporal data in description logics
 In Proc. of the International Conference on Web Reasoning and Rule Systems (RR12
, 2012
"... Abstract. Establishing a generic approach to representing and querying temporal data in the context of Description Logics (DLs) is an important, and still open challenge. The difficulty lies in that a proposed approach should reconcile a number of valuable contributions coming from diverse, yet rele ..."
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Cited by 10 (4 self)
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Abstract. Establishing a generic approach to representing and querying temporal data in the context of Description Logics (DLs) is an important, and still open challenge. The difficulty lies in that a proposed approach should reconcile a number of valuable contributions coming from diverse, yet relevant research lines, such as temporal databases and query answering in DLs, but also temporal DLs and Semantic Web practices involving rich temporal vocabularies. Within such a variety of influences, it is critical to carefully balance theoretical foundations with good prospects for reusing existing techniques, tools and methodologies. In this paper, we attempt to make first steps towards this goal. After providing a comprehensive overview of the background research and identifying the core requirements, we propose a general mechanism of defining temporal query languages for timestamped data in DLs, based on combinations of linear temporal logics with firstorder queries. Further, we advocate a controlled use of epistemic semantics in order to warrant practical query answering. We systematically motivate our proposal and highlight its basic theoretical and practical implications. Finally, we outline open problems and key directions for future research. 1