For instance, I've found work on ontology matching and ontology mapping but the application is to ontologies at the same level, i.e. a book in an ecommerce catalogue and a book in a library catalogue.
As an example of different levels of description consider the domain health with domain lung cancer. (ill)Heath and Cancer both describe the same underlying phenomena (tumours) but at different levels of description. The health level is a summary or outcome level, the cancer level is an event or process level.
Maybe it would help to think of cancer process as nested within health outcomes.
Ontology matching has a rich state-of-the-art techniques (You may also find detail information at https://hal.inria.fr/hal-00917910/document ) .
But you raise a question about challenges of "subsumption". Subsumption focuses on the mapping where one concept of an ontology is part-of another concept of different ontology.
As you said, Heath and Cancer may have same underlying phenomena, but different description. This produces subsumption relation. There are a number of researches on subsumption. You can visit the link, I added or you can google with the word "subsumption".
Thanks for answering. I did read the reference you sent Shvaiko, P. (2013). Ontology Matching : State of the Art and Future Challenges. Sactions on Knowledge and Data Engineering, 25(1), 158–176. http://doi.org/10.1109/TKDE.2011.253
I wonder if subsumption is really the right relation though. While cancer is part of health from one perspective, health and cancer have other relations - notably causal.
Another example is the relation between a car and an engine. This can not be described as subsumption because the engine is not a subclass of the car. Also, events in the car cause event in the engine (press the accelerator), and events in the engine casus events in the car (engine revving gives rise to motion).
Subsumption as example of nested hierarchical relation, causal relationship or compositional containment?
The car is composed of but the engine is not a member of the of the class car.
Cancer can be seen as a member of the class diseases = ill health. So cancer can be characterised as subsumption of diseases.
Matching and mapping are not really suitable for causal relations.
For way too long, large majority of research has been limited to the subsumption (inheritance, hierarchy) and class membership notions -- these have formal representation and there is theoretically attractive reasoning support in Description Logics. One can compute equality and inferences. Unfortunately, there are many richer relationships that we need in practice and these have been often ignored. In my view, a large majority of ontology matching/ontology alignment work can model very narrow types of situations, and is utterly useless to capture practical situations. Leroy has identified an interesting example. When I was at a telecom company, we had to different schemas: one for central office and one for the loop (line going from central office to the telephone equipment), and the same physical entity "switch" was modeled from different perspective in those two schemas.
First we need a model to characterize this situation. There has been prior models to try to support different perspective. One is Semantic Proximity in which you can explicitly capture different domains (that are modeled by respective ontologies) and different representations (captured by model "abstractions").
The following 1995 paper in VLDB Journal and a book chapter can throw some light on the challenges, but I do not want to suggest that there is an excellent solution you can easily adapt.
http://corescholar.libraries.wright.edu/cgi/viewcontent.cgi?article=1235&context=knoesis
http://knoesis.wright.edu/library/download/KS98-Semantic-Semarity-Book-Chapter.pdf
If I properly understand, the issue you rose is about multiple ontologies integration, e.g. the case of canonical anatomy and cancer diseses. If your application domain is biomedicine, you probably know Bioportal (look for the FMA and the Disease ontologies), as well as the works done at the U.S. NCBO, at the University at Buffalo (look e.g. for Barry Smith, Mathias Broachhausen), at the University of Manchester (Alan Rector, etc.), at the University of Graz (Stefan Schulz). At the German institute called IFOMIS, researchers have developed a tool for the semi-automatic integration of ontologies (look for Ulf Schwarz, and Luc Schneider). Then, you should probably investigate the use of both subsumption relationships between classes (e.g. cancer *is-a* disese), as well as specific relationships allowing you to express domain knowledge (e.g. pathologic formation *part-of* body; metastatic process *occurs-in* body, etc.. ). A very well-known paper adressing the use of relationships in ontology engineering is: Barry Smith et al., Relations in Biomedical Ontologies (http://www.genomebiology.com/content/6/5/R46). Hope this can help! Thanks for the discussion!
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