70 research outputs found

    Connected Components and Disjunctive Existential Rules

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    In this paper, we explore conjunctive query rewriting, focusing on queries containing universally quantified negation within the framework of disjunctive existential rules. We address the undecidability of the existence of a finite and complete UCQ-rewriting and the identification of finite unification sets (fus) of rules. We introduce new rule classes, connected linear rules and connected domain restricted rules, that exhibit the fus property for existential rules. Additionally, we propose disconnected disjunction for disjunctive existential rules to achieve the fus property when we extend the introduced rule fragments to disjunctive existential rules. We present ECOMPLETO, a system for efficient query rewriting with disjunctive existential rules, capable of handling UCQs with universally quantified negation. Our experiments demonstrate ECOMPLETO's consistent ability to produce finite UCQ-rewritings and describe the performance on different ontologies and queries.Comment: 23 pages, 4 figure

    Towards Ontology-Mediated Planning with OWL DL Ontologies (Extended Version)

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    While classical planning languages make the closed-domain and closed-world assumption, there have been various approaches to extend those with DL reasoning, which is then interpreted under the usual open-world semantics. Current approaches for planning with DL ontologies integrate the DL directly into the planning language, and practical approaches have been developed based on first-order rewritings or rewritings into datalog. We present here a new approach in which the planning specification and ontology are kept separate, and are linked together using an interface. This allows planning experts to work in a familiar formalism, while existing ontologies can be easily integrated and extended by ontology experts. Our approach for planning with those ontology-mediated planning problems is optimized for cases with comparatively small domains, and supports the whole OWL DL fragment. The idea is to rewrite the ontology-mediated planning problem into a classical planning problem to be processed by existing planning tools. Different to other approaches, our rewriting is data-dependent. A first experimental evaluation of our approach shows the potential and limitations of this approach.Comment: Extended version of a paper accepted at 36th International Workshop on Description Logics (DL 2023

    Saturation-based Boolean conjunctive query answering and rewriting for the guarded quantification fragments

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    Query answering is an important problem in AI, database and knowledge representation. In this paper, we develop saturation-based Boolean conjunctive query answering and rewriting procedures for the guarded, the loosely guarded and the clique-guarded fragments. Our query answering procedure improves existing resolution-based decision procedures for the guarded and the loosely guarded fragments and this procedure solves Boolean conjunctive query answering problems for the guarded, the loosely guarded and the clique-guarded fragments. Based on this query answering procedure, we also introduce a novel saturation-based query rewriting procedure for these guarded fragments. Unlike mainstream query answering and rewriting methods, our procedures derive a compact and reusable saturation, namely a closure of formulas, to handle the challenge of querying for distributed datasets. This paper lays the theoretical foundations for the first automated deduction decision procedures for Boolean conjunctive query answering and the first saturation-based Boolean conjunctive query rewriting in the guarded, the loosely guarded and the clique-guarded fragments

    A tetrachotomy of ontology-mediated queries with a covering axiom

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    Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL

    Ontology-Based Query Answering for Probabilistic Temporal Data: Extended Version

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    We investigate ontology-based query answering for data that are both temporal and probabilistic, which might occur in contexts such as stream reasoning or situation recognition with uncertain data. We present a framework that allows to represent temporal probabilistic data, and introduce a query language with which complex temporal and probabilistic patterns can be described. Specifically, this language combines conjunctive queries with operators from linear time logic as well as probability operators. We analyse the complexities of evaluating queries in this language in various settings. While in some cases, combining the temporal and the probabilistic dimension in such a way comes at the cost of increased complexity, we also determine cases for which this increase can be avoided.This is an extended version of the article to appear in the proceedings of AAAI 2019

    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

    Tuple-Generating Dependencies Capture Complex Values

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    We formalise a variant of Datalog that allows complex values constructed by nesting elements of the input database in sets and tuples. We study its complexity and give a translation into sets of tuple-generating dependencies (TGDs) for which the standard chase terminates on any input database. We identify a fragment for which reasoning is tractable. As membership is undecidable for this fragment, we develop decidable sufficient conditions

    Temporal Query Answering in DL-Lite with Negation

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    Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DL-Lite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment

    A tetrachotomy of ontology-mediated queries with a covering axiom

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    Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL
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