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**1 - 3**of**3**### The Price of Query Rewriting in Ontology-Based Data Access

"... We give a solution to the succinctness problem for the size of first-order rewritings of conjunctive queries in ontology-based data access with ontology languages such as OWL2QL, linear Datalog ± and sticky Datalog±. We show that positive existential and nonrecursive datalog rewritings, which do not ..."

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We give a solution to the succinctness problem for the size of first-order rewritings of conjunctive queries in ontology-based data access with ontology languages such as OWL2QL, linear Datalog ± and sticky Datalog±. We show that positive existential and nonrecursive datalog rewritings, which do not use extra non-logical symbols (except for inten-sional predicates in the case of datalog rewritings), suffer an exponential blowup in the worst case, while first-order rewritings can grow superpolynomially unless NP ⊆ P/poly. We also prove that nonrecursive datalog rewritings are in general exponentially more succinct than positive existential rewritings, while first-order rewritings can be super-polynomially more succinct than positive existential rewritings. On the other hand, we construct polynomial-size positive existential and nonrecursive datalog rewritings under the assumption that any data instance contains two fixed constants.

### On the Succinctness of Query Rewriting over Shallow Ontologies

"... We investigate the succinctness problem for conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial ..."

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We investigate the succinctness problem for conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial positive existential rewritings; however, in the worst case, positive existen-tial rewritings can be superpolynomial. Over ontologies of depth 2, positive existential and nonrecursive datalog rewritings of con-junctive queries can suffer an exponential blowup, while first-order rewritings can be superpolynomial unless NP ⊆ P/poly. We also analyse rewritings of tree-shaped queries over arbitrary ontologies and note that query entailment for such queries is fixed-parameter tractable. Categories and Subject Descriptors I.2.4 [Knowledge Represen-

### Combined Complexity of Answering Tree-like Queries in OWL 2 QL

"... Introduction The OWL 2 QL ontology language [11], based upon the description logic DL-LiteR, is considered particularly well suited for applications involving large amounts of data. While the data complexity of querying OWL 2 QL knowledge bases is well understood, far less is known about combined co ..."

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Introduction The OWL 2 QL ontology language [11], based upon the description logic DL-LiteR, is considered particularly well suited for applications involving large amounts of data. While the data complexity of querying OWL 2 QL knowledge bases is well understood, far less is known about combined complexity of conjunctive query (CQ) answering for restricted classes of conjunctive queries. By contrast, the combined