Towards Higher-order OWL
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PROJECT REPORT
Towards Higher‑order OWL Martin Homola1 · Ján Kľuka1 · Petra Hozzová2 · Vojtěch Svátek3 · Miroslav Vacura3 Received: 29 February 2020 / Accepted: 28 May 2020 © Gesellschaft für Informatik e.V. and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We summarize our ongoing endeavour towards proposing a suitable higher-order description logic that could serve as the semantic foundation for higher-order OWL, similarly to SROIQ serving as the semantic foundation of regular OWL. Keywords Description logics · OWL · higher-order logic
1 Introduction and motivation At the beginning there was a formally funded mobility project LAAOS: Logical Aspects of Adaptable Ontological Schemas, that our groups at Comenius University in Bratislava and University of Economics, Prague won for two years (2012–2013). A key problem addressed was rooted in the observation that different ontologies may be used to define schemas for data sets in the same domain; and the selection of the actual ontology used with a given data This work was supported from the Slovak–Czech bilateral project LAAOS supported by APVV under no. SK-CZ-0208-11 on the Slovak side and MŠMT under no. 7AMB12SK020 on the Czech side. The work was consecutively further supported by Slovak National VEGA projects no. 1/1333/12 and 1/0778/18 and on the Czech side by the EU ICT FP7 project no. 257943 (LOD2) and by the CSF project no. 18-23964S. * Martin Homola [email protected] Ján Kľuka [email protected] Petra Hozzová [email protected] Vojtěch Svátek [email protected] Miroslav Vacura [email protected] 1
Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
2
Vienna University of Technology, Favoritenstraße 9–11, Vienna 1040, Austria
3
University of Economics, Prague, W. Churchill Sq. 4, 130 67 Prague 3, Czech Republic
set may be based on different representational or reasoning complexity requirements, or by other factors. However, sometimes it is desired to translate data from one schema to another, or to integrate data sources pertaining to different schemas. Our focus in the project was on documenting the differentiating factors and heterogeneities between ontologies (which later lead to the concept of background modelling [21]), and applying ontology transformation patterns to translate and integrate data in such cases. For more details on LAAOS refer to the published overview of its immediate results [6]. During the LAAOS project we realized that many times the developers of LOD vocabularies [1] apparently intend to express higher-order classes and relations. For example, they may want to classify existing classes into (meta) classes, like saying that the tiger (which is a class, Panthera_tigris) belongs to the meta class Endagered_Species; or allowing classes to be used as subjects or as objects of a property, like saying that Yo-Yo Ma’s primary_instrument is the Cello. Such modelling practice is often referred to as metamodelling. However, OWL [5] does not really allow for this (notab
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