First-Order Rewritability and Complexity of Two-Dimensional Temporal\n Ontology-Mediated Queries Article Swipe

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Alessandro Artale , Roman Kontchakov , Alisa Kovtunova , Vladislav Ryzhikov , Frank Wolter , Michael Zakharyaschev ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2111.06806

Aiming at ontology-based data access to temporal data, we design\ntwo-dimensional temporal ontology and query languages by combining logics from\nthe (extended) DL-Lite family with linear temporal logic LTL over discrete time\n(Z,<). Our main concern is first-order rewritability of ontology-mediated\nqueries (OMQs) that consist of a 2D ontology and a positive temporal instance\nquery. Our target languages for FO-rewritings are two-sorted FO(<) -\nfirst-order logic with sorts for time instants ordered by the built-in\nprecedence relation < and for the domain of individuals - its extension FOE\nwith the standard congruence predicates t \\equiv 0 mod n, for any fixed n > 1,\nand FO(RPR) that admits relational primitive recursion. In terms of circuit\ncomplexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform\nAC0 and NC1, respectively.\n We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL\nontology languages and investigate the FO-rewritability of OMQs with atomic\nqueries by constructing projections onto 1D LTL OMQs and employing recent\nresults on the FO-rewritability of propositional LTL OMQs. As the projections\ninvolve deciding consistency of ontologies and data, we also consider the\nconsistency problem for our languages. While the undecidability of consistency\nfor 2D ontology languages with expressive Boolean role inclusions might be\nexpected, we also show that, rather surprisingly, the restriction to Krom and\nHorn role inclusions leads to decidability (and ExpSpace-completeness), even if\none admits full Booleans on concepts. As a final step, we lift some of the\nrewritability results for atomic OMQs to OMQs with expressive positive temporal\ninstance queries. The lifting results are based on an in-depth study of the\ncanonical models and only concern Horn ontologies.\n

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Computer Science

Theoretical Computer Science

Ontology

Recursion (Computer Science)

Mathematics

Programming Language

Discrete Mathematics

Artificial Intelligence

Semantic Web

Philosophy

Epistemology

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Decidability Description logic Ontology language Computer science Theoretical computer science Web Ontology Language Linear temporal logic Ontology Recursion (computer science) Consistency (knowledge bases) Temporal logic Mathematics Programming language Discrete mathematics Artificial intelligence Semantic Web Philosophy Epistemology

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Type: preprint
Landing Page: http://arxiv.org/abs/2111.06806
PDF: https://arxiv.org/pdf/2111.06806
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DOI: https://doi.org/10.48550/arxiv.2111.06806

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Title: First-Order Rewritability and Complexity of Two-Dimensional Temporal\n Ontology-Mediated Queries

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Publication year: 2021

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Publication date: 2021-11-12

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Authors: Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter, Michael Zakharyaschev

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Landing page: https://arxiv.org/abs/2111.06806

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Concepts: Decidability, Description logic, Ontology language, Computer science, Theoretical computer science, Web Ontology Language, Linear temporal logic, Ontology, Recursion (computer science), Consistency (knowledge bases), Temporal logic, Mathematics, Programming language, Discrete mathematics, Artificial intelligence, Semantic Web, Philosophy, Epistemology

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