

OntoMathPro Ontology – A hub for math knowledge - nzhiltsov
http://ontomathpro.org

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murbard2
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.

~~~
nzhiltsov
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...](https://github.com/CLLKazan/OntoMathPro/blob/master/external.links.dbpedia.nt)),
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](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.

BTW, I'd suggest using our mailing list further to keep these valuable
discussions in the proper place:
[https://groups.google.com/forum/#!forum/ontomathpro](https://groups.google.com/forum/#!forum/ontomathpro)

Next, you can submit pull requests in GitHub with suggesting improvements,
then we can discuss them there.

No offense to HN, it's just to make our life easier.

~~~
murbard2
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".

~~~
nzhiltsov
Well, your suggestion? Could you pick up the right parent element in the
ontology?

~~~
vdimarco
As I understand it, this is a good example highlighting one major challenge
for Linked Data: There can be many ways to describe a concept.

~~~
nzhiltsov
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:)

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amelius
This is really cool, but I was hoping that they were going to formalize
mathematics. For example, like this ([1]) team is doing.

Mathematics should primarily read like code, not (only) like prose.

[1]
[http://www.cs.ru.nl/~herman/FormMath.html](http://www.cs.ru.nl/~herman/FormMath.html)

~~~
nzhiltsov
Yep, there is a lot of cool stuff on formalizing maths rigorously, called
informally 'computer mathematics'. We give a brief overview of this work in
our papers.

Moreover, for the interested reader, I would suggest paying close attention to
univalent foundations of mathematics
([http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundation...](http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations.html))
introduced by Vladimir Voevodsky. It disrupts classical derivation of math
results rooted in Kantor's set theory and logics, and provides a theoretical
framework that is much more convenient for computerizing.

Unlike them, we follow the different, less theoretical and more pragmatic,
approach.

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hackuser
Applying semantic web technologies to mathematics sounds interesting, but this
project otherwise is mysterious to me. It would be much appreciated if someone
would describe what this is, what purposes it is designed to serve, what its
scope of knowledge is and for what audience (e.g., all mathematics? for
graduate-level users?). Is it ready to use or an experiment, and what tools do
I need to utilize it? (Some background on the web of data would be interesting
too.)

Perhaps I'm overlooking the obvious or I'm just uninformed in this particular
area.

~~~
nzhiltsov
Concerning scope, we focus on professional-level mathematics (Pro suffix
emphasizes that). It is ready to use, and we describe a formula search mashup
([https://github.com/CLLKazan/MathSearch](https://github.com/CLLKazan/MathSearch))
built atop of the ontology. On GitHub, you may find references to a published
RDF dataset, which was extracted automatically from a test collection of our
university's math journal.

However, I should warn that the ontology is a mature, but ongoing work (and it
is meant to be, frankly speaking, since we follow the crowdsourcing
methodology), and the quality of labels (especially, English) or coverage of
fields of mathematics should be constantly improved.

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Ih8registering2
Stuff like this reminds me of Doug Lenat's AM (automatic mathemetician) from
back in the day, written in everyone's favorite, Lisp.

~~~
nzhiltsov
To be precise, AM is related to so-called 'computer mathematics'. In this
project, we do not aim at modelling mathematics for theorem provers or similar
things. Our applications (e.g. keyword-based formula search, education,
information extraction) are introduced in the papers.

