56 research outputs found

    Loop Restricted Existential Rules and First-order Rewritability for Query Answering

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    In ontology-based data access (OBDA), the classical database is enhanced with an ontology in the form of logical assertions generating new intensional knowledge. A powerful form of such logical assertions is the tuple-generating dependencies (TGDs), also called existential rules, where Horn rules are extended by allowing existential quantifiers to appear in the rule heads. In this paper we introduce a new language called loop restricted (LR) TGDs (existential rules), which are TGDs with certain restrictions on the loops embedded in the underlying rule set. We study the complexity of this new language. We show that the conjunctive query answering (CQA) under the LR TGDs is decid- able. In particular, we prove that this language satisfies the so-called bounded derivation-depth prop- erty (BDDP), which implies that the CQA is first-order rewritable, and its data complexity is in AC0 . We also prove that the combined complexity of the CQA is EXPTIME complete, while the language membership is PSPACE complete. Then we extend the LR TGDs language to the generalised loop restricted (GLR) TGDs language, and prove that this class of TGDs still remains to be first-order rewritable and properly contains most of other first-order rewritable TGDs classes discovered in the literature so far.Comment: Full paper version of extended abstrac

    Query Rewriting and Optimization for Ontological Databases

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    Ontological queries are evaluated against a knowledge base consisting of an extensional database and an ontology (i.e., a set of logical assertions and constraints which derive new intensional knowledge from the extensional database), rather than directly on the extensional database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper, we discuss two important aspects of this problem: query rewriting and query optimization. Query rewriting consists of the compilation of an ontological query into an equivalent first-order query against the underlying extensional database. We present a novel query rewriting algorithm for rather general types of ontological constraints which is well-suited for practical implementations. In particular, we show how a conjunctive query against a knowledge base, expressed using linear and sticky existential rules, that is, members of the recently introduced Datalog+/- family of ontology languages, can be compiled into a union of conjunctive queries (UCQ) against the underlying database. Ontological query optimization, in this context, attempts to improve this rewriting process so to produce possibly small and cost-effective UCQ rewritings for an input query.Comment: arXiv admin note: text overlap with arXiv:1312.5914 by other author

    Datalog Rewritability of Disjunctive Datalog Programs and its Applications to Ontology Reasoning

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    We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog---a novel rule-based KR language that extends both datalog and linear disjunctive datalog and for which reasoning is tractable in data complexity. We then explore applications of weakly linear programs to ontology reasoning and propose a tractable extension of OWL 2 RL with disjunctive axioms. Our empirical results suggest that many non-Horn ontologies can be reduced to weakly linear programs and that query answering over such ontologies using a datalog engine is feasible in practice.Comment: 14 pages. To appear at AAAI-1

    Engineering optimisations in query rewriting for OBDA

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    Ontology-based data access (OBDA) systems use ontologies to provide views over relational databases. Most of these systems work with ontologies implemented in description logic families of reduced expressiveness, what allows applying efficient query rewriting techniques for query answering. In this paper we describe a set of optimisations that are applicable with one of the most expressive families used in this context (ELHIO¬). Our resulting system exhibits a behaviour that is comparable to the one shown by systems that handle less expressive logics

    First-order rewritability of temporal ontology-mediated queries

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    Aiming at ontology-based data access over temporal, in particular streaming data, we design a language of ontology-mediated queries by extending OWL 2 QL and SPARQL with temporal operators, and investigate rewritability of these queries into two-sorted first-order logic with < and PLUS over time

    First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

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    Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<) - first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals - its extension FOE with the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies

    Query rewriting under linear EL knowledge bases

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    With the adoption of the recent SPARQL 1.1 standard, RDF databases are capable of directly answering more expressive queries than simple conjunctive queries. In this paper we exploit such capabilities to answer conjunctive queries (CQs) under ontologies expressed in the description logic called linear EL-lin, a restricted form of EL. In particular, we show a query answering algorithm that rewrites a given CQ into a conjunctive regular path query (CRPQ) which, evaluated on the given instance, returns the correct answer. Our technique is based on the representation of infinite unions of CQs by non-deterministic finite-state automata. Our results achieve optimal data complexity, as well as producing rewritings straightforwardly implementable in SPARQL 1.1
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