research-article

Dichotomies in Ontology-Mediated Querying with the Guarded Fragment

Authors:

André Hernich,

Fabio Papacchini,

Frank WolterAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 21, Issue 3

Article No.: 20, Pages 1 - 47

https://doi.org/10.1145/3375628

Published: 20 February 2020 Publication History

Abstract

We study ontology-mediated querying in the case where ontologies are formulated in the guarded fragment of first-order logic (GF) or extensions thereof with counting and where the actual queries are (unions of) conjunctive queries. Our aim is to classify the data complexity and Datalog rewritability of query evaluation depending on the ontology O, where query evaluation w.r.t. O is in PTime (resp. Datalog rewritable) if all queries can be evaluated in PTime w.r.t. O (resp. rewritten into Datalog under O), and coNP-hard if at least one query is coNP-hard w.r.t. O. We identify several fragments of GF that enjoy a dichotomy between Datalog-rewritability (which implies PTime) and coNP-hardness as well as several other fragments that enjoy a dichotomy between PTime and coNP-hardness, but for which PTime does not imply Datalog-rewritability. For the latter, we establish and exploit a connection to constraint satisfaction problems. We also identify fragments for which there is no dichotomy between PTime and coNP. To prove this, we establish a non-trivial variation of Ladner’s theorem on the existence of NP-intermediate problems. Finally, we study the decidability of whether a given ontology enjoys PTime query evaluation, presenting both positive and negative results, depending on the fragment.

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Cited By

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https://doi.org/10.1016/j.artint.2022.103785
Gerasimova OKikot SKurucz APodolskii VZakharyaschev M(2022)A tetrachotomy of ontology-mediated queries with a covering axiomArtificial Intelligence10.1016/j.artint.2022.103738309(103738)Online publication date: Aug-2022
https://doi.org/10.1016/j.artint.2022.103738
Jung JWolter FGorla D(2021)Living without beth and craigProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470585(1-14)Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1109/LICS52264.2021.9470585

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Dichotomies in Ontology-Mediated Querying with the Guarded Fragment

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 21, Issue 3

July 2020

407 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3384674

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

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Publication History

Published: 20 February 2020

Accepted: 01 December 2019

Received: 01 April 2019

Published in TOCL Volume 21, Issue 3

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Cited By

Jung JLutz CPulcini HWolter F(2022)Logical separability of labeled data examples under ontologiesArtificial Intelligence10.1016/j.artint.2022.103785313(103785)Online publication date: Dec-2022
https://doi.org/10.1016/j.artint.2022.103785
Gerasimova OKikot SKurucz APodolskii VZakharyaschev M(2022)A tetrachotomy of ontology-mediated queries with a covering axiomArtificial Intelligence10.1016/j.artint.2022.103738309(103738)Online publication date: Aug-2022
https://doi.org/10.1016/j.artint.2022.103738
Jung JWolter FGorla D(2021)Living without beth and craigProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470585(1-14)Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1109/LICS52264.2021.9470585

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