[om] Standard .. Ontologies for Math

[Richard Fateman]

Andrew Solomon wrote:
> 
> Hmmm. Interesting. As I looked at this, I found myself wondering "why?".
> In OpenMath a primary hope is to make communication
> of mathematical objects easier.  The knowledge systems folk probably think
> it's immensely useful to be able to "share ontologies", and perhaps this
> website is more useful for that, or equivalent to STS?
> 
> As always, I applied the "semigroup" test. It fails.
> 

I don't know what the semigroup test is, but I think the motivation
for OM and knowledge systems overlap considerably.

In particular, a goal of each is to have a shared information
structure so that distinct computer systems (different software)
can agree on names, relationships, properties, of concepts like
"ring"  or "matrix" or attributes like "associative".  I think that
characterizing OM as an attempt to build a shared ontology is
not so far off the mark.  (Other than it strikes me as pompous
language.)
I looked at STS (small type system) and found it to be much less detailed than
the Stanford site for the kinds of things I might like to see
for statements of axioms and properties. But maybe I didn't
look long enough or in the right place.

 At random I poked at "NumericalValue" and found the description

"Denotes an OpenMath object that is to be thought of as a
 numerical value (possibly symbolic)."

This consists not only of a circular definition, but vaguely
suggests the possibility of a thought-crime if one disagrees,
and then suggests that a numerical value could possibly be
symbolic. (Which it is not, in my view.  But since symbolic
is not defined, who knows?)

There is no author indicated for STS.  Was this really reviewed
on 2000-09-01? By whom?


Returning to the STanford knowledge project...


I gather that this project was cut off circa 1994, most likely
shortly after using up their money from DARPA.  
RJF


> Andrew
> 
> On Thu, Jun 07, 2001 at 08:38:38AM -0700, Richard Fateman wrote:
> > I encountered recently a list of ontologies from
> > Stanford's Knowledge Systems Lab.
> > Among others, they include a framework for
> > Abstract Algebra  that might be of interest
> > to OM.
> > I suggest people (James? David?) writing CDs look around at
> > this site.
> >
> > http://piano.stanford.edu/concur/examples/html-lib/abstract-algebra/index.html
> >
> > RJF
> > --
> > om at openmath.org  -  general discussion on OpenMath
> > Post public announcements to om-announce at openmath.org
> > Automatic list maintenance software at majordomo at openmath.org
> > Mail om-owner at openmath.org for assistance with any problems
> --
> om at openmath.org  -  general discussion on OpenMath
> Post public announcements to om-announce at openmath.org
> Automatic list maintenance software at majordomo at openmath.org
> Mail om-owner at openmath.org for assistance with any problems
--
om at openmath.org  -  general discussion on OpenMath
Post public announcements to om-announce at openmath.org
Automatic list maintenance software at majordomo at openmath.org
Mail om-owner at openmath.org for assistance with any problems