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ERC

CODA Report Summary

Project ID: 647289
Funded under: H2020-EU.1.1.

Periodic Reporting for period 1 - CODA (Custom-Made Ontology Based Data Access)

Reporting period: 2015-08-01 to 2017-01-31

Summary of the context and overall objectives of the project

"We are living in an era where an unprecedented amount of data is available to companies, scientists, and individuals. Making use of this data is increasingly becoming crucial for economic success and for scientific progress, and even to take informed decisions in everyday life. However, a large amount of data from many different sources can be very difficult to handle and to interpret and, in particular, such data will often be highly incomplete and very heterogeneous in representation. How can we provide support for dealing with this situation? Imagine that a computer program which processes data has at its disposal a large amount of encyclopedic domain knowledge, of the kind provided by Wikipedia for human users. This is the purpose of an ontology and indeed ontologies have proved to be very useful for supporting the processing of incomplete and heterogeneous data. But the convenience comes at a price: processing the data and the ontology at the same time is computationally expensive. The CODA project sets out to provide an ultimately fine-grained analysis of the computational costs of ontology-mediated querying, identifying and studying "islands of tractability", that is, classes of ontologies which can be processed efficiently and have other desirable computational properties. The overall aim of this approach is to enable ontology engineers to design and customize ontologies that strike an ideal balance between the knowledge provided and efficient processing, in this way developing ontology-mediated querying to its full potential."

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The work carried out in the first reporting phase has mainly concentrated on fundamental questions of complexity and rewritability: when can an ontology-mediated query (OMQ), constituted by an ontology and an actual query, be answered in polynomial time (thus efficiently) or in AC0 (thus efficiently in parallel) and related questions; when can it be rewritten into a more traditional database query such as SQL (represented by first-order logic or by linear datalog) and into Datalog? In the first phase, we have provided elegant characterizations for many relevant cases. We have also obtained many important results on the computational complexity of the question whether a given OMQ has one of the mentioned desirable properties, thus significantly advancing our knowledge about several fundamental islands of tractability.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

So far, the knowledge about many islands of tractability in ontology-based data access has been rather incomplete and scattered. In the first phase of CODA, we have made a significant step towards a more holistic understanding of such islands, in particular those pertaining to tractability and rewritability. For ontologies from the EL family of description logics (DLs), we have brought to the picture also inverse roles and conjunctive queries (instead of only atomic ones), resulting in a rather comprehensive knowledge of the important island of FO-rewitability in the context of such DLs. For ontologies from the ALC family, we have brought to the picture conjunctive queries (instead of only atomic ones), which results in an increase of expressive power from CSP to MMSNP. We have established decidability and obtained results on the complexity of rewritability into FO and monadic Datalog, and we have made first important observations on rewritability into Datalog. On top of that, we have studied OMQ containment as a more fundamental problem, proving decidability and tight complexity bounds, and have analyzed the shape of rewritings. In the case of quantified queries, we have pushed the frontier beyond description logics by implementing a very fine-grained study of ontologies formulated in the guarded fragment, obtaining a host of results on islands of tractability defined in terms of complexity and rewritability and winning the prestigious PODS best paper award in 2017. We have also pushed the state-of-the-art regarding query inseparability, automatic termination of the chase, description logics with relations of higher arity, and first-order logics of incomplete information.
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