Three days ago we had a seminar entitled “ontologies: use and abuse” by Simone Santini (abstract, slides, video). The first part of the presentation dealt briefly with the/a definition of what an ontology is, which still sparks debate. Aside from the often-repeated definition from Gruber, there is the more comprehensive definition by Nicola Guarino  and the trimmed-down version that an ontology is a logical theory. On definitions, we still didn’t get any further than the latter; the seminar was held at the CS faculty, so that could just have influenced preference for the latter.
If you have looked at the abstract, slides, or the video, you may have noticed the absence of the efforts on terminology of ontologies etc in the bio-ontologies community. This was discussed off-line before and after the seminar, which is in no small part due to that there are no good definitions around there either. Of course, we have Barry Smith et al’s recent KR-MED article  who makes a step in that direction, but their description of an ontology–“an ontology is a representational artifact, comprising a taxonomy as proper part, whose representational units are intended to designate some combination of universals, defined classes, and certain relations between them”–is not a formal definition that would make a computer scientist happy (which may not have been the aim of the authors anyway). Moreover, and what troubles me most, is the recently published OBO Foundry paper in Nature Biotechnology . I am aware I might make some steps on thin ice for what I’m going to write, but it really is meant as an honest question—ok, a few questions.
There is not only no definition in the Nature Biotech article of what an ontology is (possibly due to the intended readership), but it starts by putting ontology in sneer quotes in the abstract. We have that “controlled vocabularies or ‘ontologies’… ” as if controlled vocabularies and ontology-in-sneer-quotes are synonyms (are they?), then there is the MGED Ontology as an “annotation resource”, which is a functional definition of sorts, but also that each OBO “Foundry ontology forms a graph-theoretic structure, with terms connected by edges representing relations”. The latter is a useful point if it weren’t for the confusion it causes because it is mentioned directly after dealing with OWL ontologies, which have a model-theoretic semantics. Now, we can have a logical theory T with model-theoretic semantics where the non-empty underlying set and interpretation (=structure) of the vocabulary (=set of function, relation, and constant symbols) happen to be a particular graph (model M). Definition-wise, we’d be making a lot of progress with that. But can an OBO Foundry ontology only be a particular graph? Why and what kind of graph, what are the properties of the graphs? Only DAGs? (Are you sure about that?) An OBO Foundry ontology can have only binary relations, or could/should that change if an n-ary (where n>2) is added to the Relation Ontology?
Also, there’s the issue of instance-level versus type-level, but we might set that aside for the moment because the OBO Foundry clearly focuses on type-level knowledge representation and we can store a type-level ontology in a database so that the universals in logical theory T are, mathematically, instances (in a model M) and pretend they are types in the GUI — so as to meet the point on having a graph as structure if we have a [TBox-] OWL ontology. Or you want to stick to obo format and DAGs instead of starting/migrating/continuing with OWL? Or have both DAGs and OWL-formalised bio-ontologies and have a definition of an ontology or, more precisely, OBO Foundry ontology, alike “a DAG or OWL-formalised logical theory”? If the latter, is there a policy for new proposals for inclusion of ontologies being represented preferably in obo format or for OWL-formalised bio-ontologies?
The article raises more questions than that it clarifies about what the OBO Foundry is after for their ontologies, but maybe I’m not the intended readership. Either way, if an OBO Foundry-paper author or member could address the questions, that would be great.
 Guarino, N. Formal ontology in information systems. Proceedings of FOIS’98, Trento, Italy, June 6-8, 1998. IOS Press, Amsterdam, pp. 3-15.
 Smith, B., Kusnierczyk, W., Schober, D., Ceusters, W. (2006). Towards a reference terminology for ontology research and development in the biomedical domain. Proceedings of KR-MED 2006, Baltimore, USA, 2006.
 Smith, B., Ashburner, M., Rosse, C., Bard, J., Bug, W., Ceusters, W., Goldberg, L.J., Eilbeck, K., Ireland, A., Mungall, C.J., The OBI Consortium, Leontis, N., Rocca-Serra, A.B., Ruttenberg, A., Sansone, S-A., Shah, M., Whetzel, P.L., Lewis, S. (2007). The OBO Foundry: Coordinated Evolution of Ontologies to Support Biomedical Data Integration. Nature Biotechnology, 25(11): 1251-1255. Free access thanks to Uni Washington (FMA group)
p.s.: thanks are due to Scott Marshall for the term “nontology” (who, admittedly, used it in a different context).