more information

Your questions ask for specificity on points that I kind of wanted to
remain flexibly general on! I am interested in this as a "general
semantic model" -- a tool for building and talking about "arbitrary"
semantic networks. At this point, I want to learn about applications
for which my proposed model will be insufficient or awkward to apply,
so I can decide whether I want to go forward with this model or use
something different.

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That said: one of the things I am most interested in at present is
developing an interactive website (i.e. this application doesn't have
a whole lot to do with language, at least in the usual sense) Here is
a sketch:

Right now PlanetMath is mainly a "mathematics reference work". I
envision it in the future being useful as a full-fledged math learning
environment. In other words, if I want to learn Abstract Algebra or
some other math topic, I should be able to log into PlanetMath and
reach some desired level of proficiency using resources I find there.

In order for this to work, the system will need to know which types of
problems I've solved, which topic-areas I seem to have mastered, which
things I need work on. All of this information can be stored as
triples, and some logic related to these assertions can guide the
user's interaction: "if Joe knows the First Isomorphism Theorem and
the Sylow theorems, then he should be able to solve problem A1287g."
If I can't solve the problem, the system needs some recourse: perhaps
it gives me an easier problem or a hint on how to solve the problem I
was given.

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A linguistics goal (this has been on the back burner for a while) is
to build a semantic parser for mathematical language -- and use this
to translate standard mathematical writing into a form that the
computer can do useful things with. For example, this parser might be
used to automatically fit new problems into the network of problems
and other information described above.

A third possible application is to use the network to implement (or to
help implement) solution heuristics, to get the computer solving the
"human style" math problems. This is very far on the horizon.

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The implementation I'm working on will run Lisp with persistent
storage via the Elephant package to Berkeley DB. Some changes to
Elephant will be needed before this will work. A "toy version" that
uses an SQL backend seems like it shouldn't be hard to finish; I may
do this today with a friend; however, Elephant plays very nice with
the Lisp object system, so I want to use that in the long run.