On Jan 27, 2009, at 10:43 AM, Jakub Kotowski wrote:  (01)
> Mitch,
>
> Mitch Harris schrieb:
>> On Tue, Jan 27, 2009 at 10:03 AM, Len Yabloko <lenya@xxxxxxxxxxxxx> 
>> wrote:
>>> Dear All
>>>
>>> Category Theory had been mentioned many times on this forum. I 
>>> think this subject deserves a separate thread. As usual the 
>>> attitudes range widely. Some of you consider CT largely irrelevant 
>>> to subjects discussed on this forum because it lacks both 
>>> philosophical underpinning of Logic and practical application of 
>>> Ontology, leaving it pretty much a mathematical discipline.
>>
>> - My opinion is that it is currently irrelevant because there are no
>> current applications of CT to ontologies
>
> I think there are some - for example the theory of institutions 
> which is
> used to study relations between different logics and therefore also
> ontologies over different logics. See:
>
> Data, Schema, Ontology and Logic Integration
> by: Joseph A Goguen
> Logic Journal of the IGPL, Vol. 13, No. 6. (November 2005), pp. 
> 685-715.
> http://dx.doi.org/10.1093/jigpal/jzi050
>
> Institutions: abstract model theory for specification and programming
> by: Joseph A Goguen, Rod M Burstall
> J. ACM, Vol. 39, No. 1. (January 1992), pp. 95-146.
> http://dx.doi.org/10.1145/147508.147524
>  (02) 
While I have the utmost respect, approaching awe, for Goguen and 
Burstall (Rod B. was one of my graduate supervisors), and while this 
stuff is often cited, I have yet to see a practical application of it. 
However, the Kestrel research institute in California 
(http://www.kestrel.edu/home/about.html 
) has been producing industrial-quality software engineering systems 
based on category-theoretic ideas for over a decade now. The 
characteristic flavor of category theory is revealed in the extremely 
rigorous typing that Kestrel's systems require, in which for example 
one is obliged to distinguish between the integer, real and rational 
versions of zero. These are distinct in category theory, which pays 
careful attention to domains and ranges of even the most 'trivial' 
functions.  (03)
PatH  (04)
> Jakub
>
>> , and I don't see any
>> immediate applications other than loose analogies. Sure, some
>> application might be developed, but right now I don't see any (but
>> please don't that let prevent people from at least considering it).
>>
>
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>  (05) 
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