John Sowa wrote:
> Dear Matthew,
>
> I agree with your points. I'd like to add some comments and give
> a historical example of the way a simple theory develops over time
> into a large family (a hierarchy) of related theories.
>
> JFS>> There is no [stage in the development of an ontology] that is
> >> "just enough" for *all* applications. Cyc, for example, found
> >> that no matter how much knowledge they have formalized over the
> >> past 26 years, they can't get up to a level that is "enough".
> >> Every new application requires more. (01)
> MW> What this does is change the problem slightly from actually having
> > an ontology that does capture everything, to having an ontology that
> > is easily extensible when things are found that are beyond its current
> > scope. (02)
JFS> I agree. But if you think of a ontology as a single, unified theory,
> then you have many thorny issues about what it means to be extensible. (03)
An ontology with a single theory would complicate the idea of a
foundational ontology as an interlingua to which all external ontologies
can be mapped. Competing external theories could be incorporated by
defining new concepts/relations for the relata of the competing theories
(which map directly to the terms of the source ontology) and then adding
rules relating them with the ostensible "sameAs" terms already in the
foundational ontology. (04)
JFS> But if you think of an ontology as a collection of theories organized
> in a hierarchy, no single theory ever changes. Instead, each innovation
> adds another theory to the hierarchy, which may be a generalization,
> a specialization, a sibling, or a cousin of some other theory. You
> can also compare and combine theories. (05)
Agreed. This is part of the reasoning behind Cyc method of "microtheories"
or contexts. (06)
Cyc has multiple types of "microtheories". Several of these categories
relate to this discussion:
* Vocabulary microtheories: Provide basic definitional statements about
ontological terms.
* Theory microtheories: Provide rules on the interaction of components
in an ontology.
* Data microtheories: Basically, knowledge bases. These provide data
about individual instances of the types defined in a vocabulary micro-
theory and statements using the relations defined therein. The data
microtheory might have temporal restrictions (the prices defined in
this MT are valid from 1 JAN 2010 to 31 MAR 2010), regional restrictions
(this weather forcast is restricted to Galway, Ireland), or other
restrictions.
* Query microtheories: Temporary contexts are defined, given a set of
data, theory, and associated vocabulary microtheories to be used, and
possibly some new facts (or hypotheses) are added. Questions are asked
and reasoning produces answers using the statements in the available
microtheories. (07)
> MW> Another thing that falls out from this is how you deal with context.
> > By this I mean what is left implicit. Making the context explicit
> > becomes increasingly important if you want to adopt this approach. (08)
JFS> Yes, you can think of context as some additional statements S that are
> added to a theory T to specialize it for some particular application. (09)
If the context referred to is what Cyc calls a DataMicrotheory, then
the statements added are qualitatively different from those in the basic
theory. (010)
A context might close T's open world assumption, such that T2 has a
closed world assumption. T and T2, in such a case, would be different types
of theory. (011)
JFS> But there are also many other reasons for adding more statements.
> In terms of the hierarchy, the deductive closure of T with more
> statements S is a new theory T2 that is placed below the original T. (012)
> JFS>> But for any given set of applications, it is not too difficult
> >> to formalize just enough for those applications.
>
> MW> Doing this for a known set of applications is relatively easy.
> > The challenge is to enable arbitrary addition of applications. (013)
> I agree. And my suggestion for supporting an open-ended number of
> applications of any kind is to organize the collection of theories
> in a hierarchy. Any change of any kind can be accommodated by
> inserting a generalization, specialization, sibling, or cousin. (014)
I agree. An FO would need to have a reasonably restrictive generalization
of classes included in any microtheory that is to be mapped to it. Defining
"reasonably restrictive" could be hard, but it seems to me that SUMO (with
extensions) and Cyc both would currently meet this requirement. Including
concepts from UMLS and GoodRelations would lower the rough lower edge of
the directed acyclic graph of classes in several key areas. (015)
One question is on what basis should individuals should be included in an
FO. Certainly units of measure should be. Currencies & countries surely.
Cities and every instance in the GeoNames base? How should the selection
of people to add be made? Organizations? Conceptual works (books, movies,
songs, albums, paintings, constitutions, poems, ...)? Sports and games?
Events (disasters, wars, elections, mergers, ...)? Etc. (016)
If the FO is to include such things, there are sources for lists of members
of such categories. Many already have URIs for the terms. But at least
some of these sources would have to be carefully vetted. Among the tens
of thousands of such instances in OpenCyc, for example, there are numerous
instances of hypothetical persons, organizations, and events (presumably
originally from hypothetical contexts) that are not identified as
hypothetical but one would not want to include. (017)
The breadth of coverage of the proposed FO needs to clarified. Is it to be
an ever-expanding set of all terms defined in any ontology? Should it
include all individuals ever defined on the Semantic Web? (018)
Or could there be a basic, relatively fixed, FO to which an expanding
number of contextually restricted, but still centralized, ontologies are
related? I could see such for brand-name products, GeoNames, UMLS, IMDB,
GeneBase, etc. (019)
-- doug (020)
> [History of the development of set theory] (021)
> This story illustrates the basic ways in which theories evolve,
> and that's the framework I proposed for ontologies:
>
> http://www.jfsowa.com/pubs/dynonto.htm
> A Dynamic Theory of Ontology
>
> John (022)
=============================================================
doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (023)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
============================================================= (024)
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