I'm really glad this is happening. I looked for such a thing a few months ago and couldn't find it. This morning, the authors mentioned it on my math.stackexchange question.
For me, one of the motivation it to be able to draw dependency graphs to understand each concept clearly.
However, I have a feeling that some of this was extracted automatically from Wikipedia and needs curation. For instance "Markovian chain" has, as a superclass, "Elements of probability theory". Hum no. "Markovian chain" is NOT a kind of "Elements of probability theory". You could argue it is an element of probability theory (which is a rather vague term), but then the plural would have to be dropped. I also haven't seen any example of multiple inheritance, which would be absolutely critical to describe most interesting mathematical objects.
In general, since this is using a description language, the semantic of inheritance seems like a weak choice to describe the often more subtle relationships that exist between mathematical objects.
Hi, nice to here. I'm a co-author. Let me clarify some of your points.
1) Indeed, we consider visualization of graph dependencies in OntoMathPro as an important application for learning. Given sufficient coverage of relationships between concepts, it can provide a helpful context for any non-trivial term.
2) No, the ontology was constructed collaboratively and manually from scratch, and Wikipedia was just one of the used resources. BTW, overlapping between the math part of Wikipedia (or DBpedia as we think in terms of Linked Data) and OntoMathPro is saved in the mapping file (https://github.com/CLLKazan/OntoMathPro/blob/master/external...), which was extracted automatically afterwards.
3) Concerning "ElementS of Probability Theory", could you please provide class URI you are talking about? Because I can see only this relevant one: E2406 http://ontomathpro.org/ontology/E2406___599545262.html which has the proper name (without 's').
4) We do allow and have multiple inheritance. Please see E1892 Differential Equation, which is a sub-class of both E1891 Equation and E2688 Element of Differential Equations. I believe there are more subtle examples in the ontology (can't remember exactly for now).
5) About ontology engineering principles, if you are interested in, please peruse our research papers (especially, [2]), in which we elaborate our modeling principles.
6) I can't agree about 'weakness' of the chosen language. OWL 2 is quite expressive to provide non-trivial logical rules and properties. For examples, some of them are already in place: P5 'see also' property is transitive and symmetric. Surely, we can't describe the precise semantics of mathematics (we would have to have a more expressive language than mathematics itself according to Popper's methodology). But we don't need it to build fascinating applications atop of the existing ontology, as our work hopefully shows.
3) My bad, I don't know why I read it with an S... strange.
6) No, OWL is very powerful, my point is about the choice of vocabulary... For instance, a markov chain is not an "element of probability theory" in the same way as it is a "probabilistic model" or a "stochastic process".
I would say this is by no means a flaw of Linked Data (the Semantic Web approach). There is an essential duality in many domains, including mathematics. For example, we can adhere different approaches to describe the math theory as a whole from the following points of view:
1) Classical (N. Burbaki's approach): Kantor's set theory and logic
2) Constructive: where we are standing on constructive (intuitionistic) logic
3) Univalent foundations of mathematics (a novel approach).
Even if we stick to the 1st approach only (as we did for the ontology), there are also many dualities (alternative definitions), if we apply, say, terminology from geometry or, alternatively, from set theory while describing the same math objects.
Anyway, I think the methodology, we are working on during this project, should clarify many such hidden aspects. And we expect that it will be valuable for the modern math theory itself. So, let's collaborate:)
For me, one of the motivation it to be able to draw dependency graphs to understand each concept clearly.
However, I have a feeling that some of this was extracted automatically from Wikipedia and needs curation. For instance "Markovian chain" has, as a superclass, "Elements of probability theory". Hum no. "Markovian chain" is NOT a kind of "Elements of probability theory". You could argue it is an element of probability theory (which is a rather vague term), but then the plural would have to be dropped. I also haven't seen any example of multiple inheritance, which would be absolutely critical to describe most interesting mathematical objects.
In general, since this is using a description language, the semantic of inheritance seems like a weak choice to describe the often more subtle relationships that exist between mathematical objects.