Re: SUO: Lattice of Theories vs a Single Ontology
Adam,
I think you should be able to do just as you suggest, put things in
different files. However, the real value of such an arrangement is on
the representation level. You are creating modular theories. You now can
deal with local consistency and local completeness, i.e., theory X is
consistent, theory Y is consistent, but taken together they are
inconsistent: why? Maybe because you can focus on a subset: X has A,B;
Y has A, -B. Therefore they are consistent on A. Hence, create a theory
Z which has A (or have your "intelligent" system which knows about the
logical properties of theories/ontologies do so for you). Z can be
viewed as the intersection of X and Y or as the meet of X and Y if they
inhere in a lattice. The point is that X, Y, Z, are partially ordered
theories or something stronger, part of a lattice.
In fact, contrary to your guess, I think there are many highly separable
components: a theory of mereotopology and variants (other theories with
more or less axioms), a theory of
collectivity-distributivity-cumulativity (for plurals, masses,
organizations, etc., which will probably build on the mereotopology
theories), theories of time (scalar, branching, point, interval),
theories of events (processes, actions, states), theories of space,
location, emotion, agency, planning, language, etc. And, as you go
downwards, toward domain theories/ontologies, separability increases. A
theory about military command and control is very distinct from a theory
of business-to-business e-commerce, though of course they share
theories.
Again, this is mostly viewing things "semantically" (slight misnomer,
since theories are syntactic, models are semantic; please forgive since
when I see theories, I see models). I also think you can view things
"syntactically". For example, given a monolithic ontology, try to use
syntactic (weak) methods to partition the knowledge (into "theories" or
knowledge partitions) by using graph-theoretic methods (e.g., graph
partitioning, see for example, the recent work by John McCarthy, Eyal
Amir, Sheila McIlraith, et al., 2000, 2001). In this view, you don't
know if you have distinct "theories". I know a bit about this approach
because I proposed similar research a couple years back. I think you
Adam may also be involved in comparable work, related to knowledge
compilation: if you can partition a knowledge base/ontology, then you
can have different "target" languages for those partitions and compile
the knowledge to meet those targets. I know OntologyWorks(Bill Anderson
et al) uses these notions too.
Also, of course, the notion of a lattice of theories has a correlate in
possible worlds. These worlds are usually related via accessibility
relations (which may be consequence or satisfaction relations). In the
lattice of theories framework, one can gauge the "distance" between
worlds, i.e., the distance between one theory and another. I know this
notion will possibly offend many formalists and modal logicians, so I
don't want to push it too far. But "belief" systems are similar. This
kind of overall framework is expressible in category theory.
Leo
Adam Pease wrote:
>
> Leo,
> You're right that it's intuitively easy but I think what both Mike and I
> are trying to get at is what is the actual advantage of such an arrangement
> in practice. If this just means that we put separable theories in
> different files, or well-delineated sections of the same file that sounds
> very reasonable to me. However, I suspect there are few such highly
> separable components.
>
> Adam
>
> At 08:59 PM 8/23/2001 -0400, Leo Obrst wrote:
> >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
> > >
> > >
> > ******************************************************************************
> > > NB: If you send email to me
> > > 1. from outside the Boeing Company or
> > > 2. from inside the Boeing Company, but not using Exchange
> > > Then, as of August 24 2001 you must use the following email
> > > address: michael.f.uschold@boeing.com. Other addresses,
> > > such as mfu@redwood.rt.cs.boeing.com or
> > > michael.f.uschold@PSS.boeing.com won't work.
> > > Please update your email address books accordingly.
> > >
> > ******************************************************************************
> > >
> > > -----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
> >Voice: 703-883-6770 7515 Colshire Drive, M/S W640
> >Fax: 703-883-1379 McLean, VA 22102-7508, USA
>
> Adam Pease
> Teknowledge
> (650) 424-0500 x571
--
_____________________________________________
Dr. Leo Obrst The MITRE Corporation
mailto:lobrst@mitre.org Intelligent Information Management/Exploitation
Voice: 703-883-6770 7515 Colshire Drive, M/S W640
Fax: 703-883-1379 McLean, VA 22102-7508, USA