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arXiv · 1611.02453

The Data Complexity of Description Logic Ontologies

Carsten Lutz·Frank Wolter
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Abstract

We analyze the data complexity of ontology-mediated querying where the ontologies are formulated in a description logic (DL) of the ALC family and queries are conjunctive queries, positive existential queries, or acyclic conjunctive queries. Our approach is non-uniform in the sense that we aim to understand the complexity of each single ontology instead of for all ontologies formulated in a certain language. While doing so, we quantify over the queries and are interested, for example, in the question whether all queries can be evaluated in polynomial time w.r.t. a given ontology. Our results include a PTime/coNP-dichotomy for ontologies of depth one in the description logic ALCFI, the same dichotomy for ALC- and ALCI-ontologies of unrestricted depth, and the non-existence of such a dichotomy for ALCF-ontologies. For the latter DL, we additionally show that it is undecidable whether a given ontology admits PTime query evaluation. We also consider the connection between PTime query evaluation and rewritability into (monadic) Datalog.

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Carsten Lutz, Frank Wolter. 2016-11-08. The Data Complexity of Description Logic Ontologies. https://doi.org/10.23638/lmcs-13(4%3A7)2017

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