Re: SUO: Lattice of Theories vs a Single Ontology
It's intuitively easy: given an ontology with A, B, C, and an ontology
with X, Y, Z, create another ontology with A, B, Y, Z. That is, take a
subset of what you need from one ontology and a subset from another (ok,
maybe a partially ordered subset): axioms and theorems. Now, you will
also need to correlate those possibly (i.e., state some
consistency-preserving equivalences). This is why the lattice/poset
(depends on the properties you want) of theories is closely correlated
to the notion of formalized contexts. This "third ontology" is now able
to be used by anyone else who has the same needs, and it's logically
related to its "base" theories.
I can give you some citations on "Little theories", using theory
interpretation in a simple type theory (less general than category
theory) in which theories are interrelated, since I've recently looked
at these. Theory interpretations are syntactic transformations which
preserve theorems. Note that in category theory both a theory and its
interpretation are objects related by morphisms, as in Barwise's
Information Flow Theory and Bob Kent's IFF (which may not be clear).
W. M. Farmer, J. D. Guttman, and F. J. Thayer. 1992. In: D. Kapur, ed.,
Automated Deduction--CADE-11, LNCS, 607:567-581, 1992.
http://imps.mcmaster.ca/doc/intertheory.pdf
W. M. Farmer. 2000. In: D. McAllester, ed., Automated
Deduction--CADE-17, LNCS, 1831:115-131, 2000. An infrastructure for
intertheory reasoning. http://imps.mcmaster.ca/doc/intertheory.pdf
W. M. Farmer. 1996. Perspective switching using theories and
interpretations. In: J. Albus, A. Meystel, and R. Quintero, eds.,
Intelligent Systems: A Semiotic Perspective, Vol. I, pp. 206-207,
National Institute of Standards and Technology, Gaithersburg, MD,
October 20-23, 1996. Abstract.
http://imps.mcmaster.ca/doc/perspect-switching.pdf
All of these (and more) are at:
http://imps.mcmaster.ca/wmfarmer/publications.html
Leo
"Uschold, Michael F" wrote:
>
> John,
>
> Perhaps you could help us all understand the lattice idea better, by coming up with a good example using some of what SUMO has already, as well as what are competing and inconsistent approaches. E.g. 3d vs 4d view, or pick your favorite examples. Personally, I think the lattice idea is a good one, but it would be good to see examples of it working.
>
> I tend to think that the lattice idea, in all it's glory, which is to say, that covers a substantial body of knowledge in a neat and tidy way will take much much longer to do than to build one ontology, which for all its shortcomings, has the advantage of existing in some reasonable time scale, and can start to be used. Perhaps we have an 80/20 situation here. 80% of the value can be had by building a single ontology with reasonable coverage. It will tak 80% of the effort to include all the rest of the sometimes incompatible theories (including methods for building larger theories from choosing smaller ones) in a beautiful lattice. So perhaps we can come to some sort of (perhaps violent) agreement here. I.e. that it is a good idea to build a single ontology to start with, but to recognize that any one single ontology will have important things missing. The loonger term effort can be to create the wonderfull lattice of theories of everything. It might be done by adding to !
th!
> e starter one, or not.
>
> Mike
>
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>
> -----Original Message-----
> From: John F. Sowa [mailto:sowa@bestweb.net]
> Sent: Thursday, August 23, 2001 1:48 PM
> To: Adam Pease
> Cc: Yang Yun; standard-upper-ontology@ieee.org; phayes@ai.uwf.edu
> Subject: Re: SUO: 2000-7-26 example
>
> Adam,
>
> This is just the tiny nose of the camel creeping under the SUMO tent:
>
> > We can map domain-specific words to concepts in the SUMO much in the same
> > way the WordNet mapping is being performed using synonymousExternalConcept
> > etc.
>
> Of course you can, but WordNet doesn't attempt to give the axioms.
> That is where all the problems are.
>
> > In SUMO Human is a distinct class from Group. We should add an axiom to
> > Group though that constrains it to require more than one member and Ian is
> > doing that just now.
>
> Yes, but one has to add a thousand buts.... And I don't believe that
> Ian is going to be able to handle them all. The lattice allows a
> collaborative development in a way that a monolithic ontology can
> never support.
>
> Furthermore, in Ian's presentation at IJCAI, he threw out the categories
> of Fistness, Secondness, and Thirdness (or Independent, Relative, and
> Mediating). And those happen to be exactly the ones you need to define
> what it means to be an executive. They also are needed to define what
> it means to be a team, a business, a government, an institution, or
> a society instead of just a simple collection.
>
> I don't blame Ian for throwing them out, because he didn't know exactly
> what to do with them at the time. But I blame you (Adam) for claiming
> that what he has is sufficient (or will ever be sufficient if he
> continues in the way he is going).
>
> Bottom line: If you had a lattice, Ian could continue as long as he
> likes working on his part of the lattice while other people could
> develop other parts, such as the theory of social groups and their
> interactions, and they could be merged at a later date.
>
> John Sowa
--
_____________________________________________
Dr. Leo Obrst The MITRE Corporation
mailto:lobrst@mitre.org Intelligent Information Management/Exploitation
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