quantMD: Ontology-Based Management for Many-Dimensional Quantitative Data

Lead Research Organisation: Birkbeck, University of London
Department Name: Computer Science and Information Systems

Abstract

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Description We have made significant progress towards our goal of extending standard static ontology-based data access to data with a temporal dimension.

We started by developing a framework for querying one-dimensional temporal data that can represent the temporal evolution of a single object. We take into account brackground knowledge formulated in an ontology. We proposed to use ontologies given in linear temporal logic, LTL, which has been invented in philosophy and has been successfully applied in computer science in the area of program verification. Queries are also given in the positive fragment of LTL. Within this framework, we investigated the complexity and rewritability of ontology-mediated queries into standard relational database queries in SQL. By taking account of the expressivity of the temporal operators used in the ontology and the shape of the queries, we identified a hierarchy of more and more powerful ontology-mediated queries and proved rewritability into either standard database queries, such queries extended by standard arithmetic predicates, and further extensions with primitive recursion. We also investigated the computational complexity of the problem of deciding whether a given ontology-mediated query is rewritable to this or that extension of SQL. We have thus laid the foundation for practical ontology-based access to one-dimensional temporal data.

In a second step, we extended our framework for querying one-dimensional temporal data to querying two-dimensional data, in which each timestamp comes with a database base of facts that are true at that timestamp. We propose to model the second dimension using the description logic underpinning the OWL profile for static one-dimensional data access standardized by the W3C. Within this framework, we prove powerful transfer results that lift our complexity and rewritability results from the one-dimensional to the two-dimensional case. Using these transfer results we obtain again a hierarchy of more and more powerful two-dimensional ontology-mediated queries that combine fragments of LTL with description logic.

Another possible two-dimensional language for temporal ontology-based data access we proposed in this project is datalogMTL that combines standard atemporal datalog with operators of metric temporal logic MTL.
Finally, we found a solution to a long-standing open problem on the complexity of recognising boundedness of monadic datalog queries with a single recursive rule.
Exploitation Route Our results lay the foundations for querying many-dimensional data modulo ontologies. They have already partly been used to support aggregate queries and temporal datatypes in the commercial ontology-based data access system Ontop. Our new techniques might be applied in the future to analyse even more expressive ontology and query languages. They might also be used to develop query answering algorithms for even more expressive languages and implement them in systems.
Sectors Digital/Communication/Information Technologies (including Software)
 
Description Our research has contributed to the development of the commercial system Ontop. Ontop is a Virtual Knowledge Graph system, which exposes the content of arbitrary relational databases as ontologies or knowledge graphs. These ontologies/graphs are virtual, which means that data remains in the data sources instead of being moved to another database. Since 2019, Ontop is developed and commercialised by the start-up company Ontopic which is based in Bolzano, Italy. Our research in this project contributed, for instance, to the addition of aggregate queries and datatypes for modelling temporal data to Ontop. Our research has also contributed to the development of ontology-based access approach to temporal log data. This approach is based on a datalog extension datalogMTL of metric temporal logic. It is now being implemented and evaluated in a reasoner MeTeoR at the University of Oxford.
First Year Of Impact 2021
Sector Digital/Communication/Information Technologies (including Software)
Impact Types Economic