[om] Standard .. Ontologies for Math

Andrew Solomon andrew at illywhacker.net
Sat Jun 9 21:34:46 CEST 2001

I feel the need to clarify something from this recent exchange.

I 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?

and RJF replied:
> 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 would like to make it clear that I agree with this but my feeling
is that computer algebra systems are a long way from being able
to import ontologies, learning about new concepts from some
external database. The only possibility
I see at this time is for a theorem prover (which probably *can* import
ontologies) to manage a bunch of CAS as "proof agents", using each 
if its ontology includes some object at hand. 

I also want to make it clear that I referred to the "knowledge systems folk"
not as distinct from the OpenMath community, but only as distict from me.

best wishes,

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