62 research outputs found

    Query Rewriting with Disjunctive Existential Rules and Mappings

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    We consider the issue of answering unions of conjunctive queries (UCQs) with disjunctive existential rules and mappings. While this issue has already been well studied from a chase perspective, query rewriting within UCQs has hardly been addressed yet. We first propose a sound and complete query rewriting operator, which has the advantage of establishing a tight relationship between a chase step and a rewriting step. The associated breadth-first query rewriting algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive query that has no UCQ-rewriting. It follows that the notion of finite unification sets (fus), which denotes sets of existential rules such that any UCQ admits a UCQ-rewriting, seems to have little relevance in this setting. Finally, turning our attention to mappings, we show that the problem of determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping is undecidable. We conclude with a number of open problems.Comment: This report contains the paper accepted at KR 2023 and an appendix with full proofs. 24 page

    Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic

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    Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete

    Decidability of Querying First-Order Theories via Countermodels of Finite Width

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    We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of width measures (with treewidth and cliquewidth as popular examples). As an important special case of our framework, we identify logics exhibiting width-finite finitely universal model sets, warranting decidable entailment for a wide range of homomorphism-closed queries, subsuming a diverse set of practically relevant query languages. As a particularly powerful width measure, we propose Blumensath's partitionwidth, which subsumes various other commonly considered width measures and exhibits highly favorable computational and structural properties. Focusing on the formalism of existential rules as a popular showcase, we explain how finite partitionwidth sets of rules subsume other known abstract decidable classes but -- leveraging existing notions of stratification -- also cover a wide range of new rulesets. We expose natural limitations for fitting the class of finite unification sets into our picture and provide several options for remedy

    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

    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

    From Horn-SRIQ to Datalog: A Data-Independent Transformation that Preserves Assertion Entailment: Extended Version

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    Ontology-based access to large data-sets has recently gained a lot of attention. To access data e_ciently, one approach is to rewrite the ontology into Datalog, and then use powerful Datalog engines to compute implicit entailments. Existing rewriting techniques support Description Logics (DLs) from ELH to Horn-SHIQ. We go one step further and present one such data-independent rewriting technique for Horn-SRIQ⊓, the extension of Horn-SHIQ that supports role chain axioms, an expressive feature prominently used in many real-world ontologies. We evaluated our rewriting technique on a large known corpus of ontologies. Our experiments show that the resulting rewritings are of moderate size, and that our approach is more efficient than state-of-the-art DL reasoners when reasoning with data-intensive ontologies.This is an extended version of the article to appear in the proceedings of AAAI 2019

    Automated Deduction – CADE 28

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    This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

    28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

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    The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond
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