It’s a topic that never failed to generate a discussion on all 10 instalments of the ontology engineering course I taught from BSc(hons) up to participants studying toward or already having a PhD: those pesky definitions of what an ontology is. To top it off, like I didn’t know, I also got a snarky reviewer’s comment about it on my Stuff ontology paper :
A comment that might be superficial but I cannot help: since an ontology is usually (in Borst’s terms) assumed to be a ‘shared’ conceptualization, I find a little surprising for such a complex model to have been designed by a sole author. While I acknowledge the huge amount of literature carefully analyzed, it still seems that the concrete modeling decisions eventually relied on the background of a single ontologist
Is that bad? Does that make the Stuff Ontology a ‘nontology’? And, by the by, what about all those loner philosophers who write single-author papers on ontology; should that whole field be discarded because most of the ontology insights were “shared” only from paper submission and publication?
Anyway, let’s start from the beginning. There’s the much-criticized definition of an ontology from Gruber that, it seems, only novices seem to keep quoting (to my irritation, indeed):
An ontology is a specification of a conceptualization. 
If you wonder why quite a bit has been written about it: try to answer what “specification” really means and how it is specified, and what exactly a “conceptualization” is. The real fun starts with Borst et al.’s  and then Studer et al.’s  refinement of Gruber’s version, which the reviewer quoted above alluded to:
An ontology is a formal, explicit specification of a shared conceptualization. 
At least there’s the “formal” (be it in the sense of logic or formal ontology), and “explicit”, so something is being made explicit and precise. But “shared”? Shared with whom? How? Is a logical theory that not one, but two, people write down an ontology, then? Or one person develops an ontology and then emails it to a few colleagues or puts it online in, say, the open BioPortal ontology repository. Does that count as “shared” then? Or is it only “shared” if at least one other person agrees with it as is (all reviewers of the Stuff Ontology did, btw), or perhaps (most or all of) the ‘conceptualization’ of it but a few axioms would need a bit of tweaking and cleaning up? Do you need at least a group of people to develop an ontology, and if so, how large should that group be, and should that group consist of independent sub-groups that adopt the ontology (and if so, how many endorsers)? Is a lightweight low-hanging-fruit ontology that is used by a large company a real or successful ontology, but a highly axiomatised ontology with a high tangledness that is used by a specialist organization, not? And even if you canvass and get a large group and/or organization to buy into that formal explicit specification, what if they are all wrong on the reality is supposed to represent? Does it still count as an ontology no matter how wrong the conceptualization is, just because it’s formal, explicit, and shared? Is a tailor-made module of, say, the DOLCE ontology not also an ontology, even if the module was made by one person and made available in an online repository like ROMULUS?
Perhaps one shouldn’t start top-down, but bottom-up: take some things and decide (who?) whether it is an ontology or not. Case one: the taxonomy of part-whole relations is a mini-ontology, and although at the start only ‘shared’ with my co-author and published in the Applied Ontology journal , it has been used by quite a few researchers for various (and unintended) purposes afterward, notably in NLP (e.g., ). An ontology? If so, since when? Case two: Noy et al. converted the representation of the NCI thesaurus into OWL DL . Does changing the serialisation of a multi-authored thesaurus from one format into another make it an ontology? (more on that below.) Case three: a group of 5 people try to represent the subject domain of, say, breast cancer, but it is replete with mistakes both regarding the reality it ought to represent and unintended modelling errors (such as confusing is-a with part-of). Is it still an ontology, albeit a bad one?
It gets more muddled when the representation language is thrown in (as with case 2 above). What if the ontology turns out to be unsatisfiable? From a logic viewpoint, it’s not a theory then (a consistent set of sentences, is), but if it’s formal, explicit, and shared, is it acceptable that those people who developed the artefact simply have an inconsistent conceptualization and that it still counts as an ontology?
Horrocks et al.  simplify the whole thing by eliminating the ‘shared’ aspect:
an ontology being equivalent to a Description Logic knowledge base. 
However, this generates a set of questions and problems of its own that are practically also problematic. For instance: 1) whether transforming a UML Class Diagram into OWL ‘magically’ makes it an ontology (answer: no); 2) The NCI Thesaurus to OWL (answer: no); or 3) if you used, say, Common Logic to represent it, that then it could not be an ontology because it’s not formalised in Description Logics (answer: it sure can be one).
There are more attempts to give a definition or a description, notably by Nicola Guarino in  (a key paper in the field):
An ontology is a logical theory accounting for the intended meaning of a formal vocabulary, i.e. its ontological commitment to a particular conceptualization of the world. The intended models of a logical language using such a vocabulary are constrained by its ontological commitment. An ontology indirectly reflects this commitment (and the underlying conceptualization) by approximating these intended models. 
That’s a mouthful, but at least no “shared” in there, either. And, finally, among the many definitions in , here’s Barry Smith and cs.’s take on it:
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. 
And again, no “shared” either in this definition. Of course, also with Smith’s definition, there are things one can debate about and pose it against Guarino’s definition, like the “universals” vs. “conceptualization” etc., but that’s a story for another time.
So, to sum up: there is that problem on how to interpret “shared”, which is untenable, and one just as well can pick a definition of an ontology from a widely cited paper that doesn’t include that in the definition.
That said, all this doesn’t help my students to grapple with the notion of ‘an ontology’. Examples help, and it would be good if someone, or, say, the International Association for Ontology and its Applications (IAOA) would have a list of “exemplar ontologies” sooner rather than later. (Yes, I have a list, but it still needs to be annotated better). Another aspect that helps explaining it comes is from Guarino’s slides on going “from logical to ontological level” and on good and bad ontologies. This first screenshot (taken from my slides—easier to find) shows there’s “something more” to an ontology than just the logic, with a hint to reasons why (note to my students: more about that later in the course). The second screenshot shows that, yes, we can have the good, bad, and ugly: the yellow oval denotes the intended models (what it should be), and the other ovals denote the various approximations that one may have tried to represent in an ontology. For instance, representing ‘each human has exactly one brain’ is more precise (“good”) than stating ‘each human has at least one brain’ (“less good”) or not saying anything at all about it an ontology of human anatomy (“bad”), and even “worse” it would be if that ontology ware to state ‘each human has exactly two tails’.
Maybe we can’t do better than ‘intuition’ or ‘very wieldy explanation’. If this were a local installation of WordPress, I’d have added a poll on definitions and the subjectivity on the shared-ness factor (though knowing well that science isn’t governed as a democracy). In lieu of that: comments, preferences for one definition or the other, or any better suggestions for definitions are most welcome! (The next instalment of my Ontology Engineering course will start in a few week’s time.)
 Keet, C.M. A core ontology of macroscopic stuff. 19th International Conference on Knowledge Engineering and Knowledge Management (EKAW’14). K. Janowicz et al. (Eds.). 24-28 Nov, 2014, Linkoping, Sweden. Springer LNAI vol. 8876, 209-224.
 Gruber, T. R. A translation approach to portable ontology specifications. Knowledge Acquisition, 1993, 5(2):199-220.
 Borst, W.N., Akkermans, J.M. Engineering Ontologies. International Journal of Human-Computer Studies, 1997, 46(2-3):365-406.
 Studer, R., Benjamins, R., and Fensel, D. Knowledge engineering: Principles and methods. Data & Knowledge Engineering, 1998, 25(1-2):161-198.
 Keet, C.M., Artale, A. Representing and Reasoning over a Taxonomy of Part-Whole Relations. Applied Ontology, 2008, 3(1-2):91-110.
 Tandon, N., Hariman, C., Urbani, J., Rohrbach, A., Rohrbach, M., Weikum, G.: Commonsense in parts: Mining part-whole relations from the web and image tags. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI’16). pp. 243-250. AAAI Press (2016)
 Noy, N.F., de Coronado, S., Solbrig, H., Fragoso, G., Hartel, F.W., Musen, M. Representing the NCI Thesaurus in OWL DL: Modeling tools help modeling languages. Applied Ontology, 2008, 3(3):173-190.
 Horrocks, I., Patel-Schneider, P. F., and van Harmelen, F. From SHIQ and RDF to OWL: The making of a web ontology language. Journal of Web Semantics, 2003, 1(1):7.
 Guarino, N. (1998). Formal ontology and information systems. In Guarino, N., editor, Proceedings of Formal Ontology in Information Systems (FOIS’98), Frontiers in Artificial intelligence and Applications, pages 3-15. Amsterdam: IOS Press.
 Smith, B., Kusnierczyk, W., Schober, D., Ceusters, W. Towards a Reference Terminology for Ontology Research and Development in the Biomedical Domain. KR-MED 2006 “Biomedical Ontology in Action”. November 8, 2006, Baltimore, Maryland, USA.