> > >
> Jeffrey Schiffel originally
wrote:
> > >
>
> > >
>... A system is smaller than
the world. A system of systems
> > >
> is still very small compared to the world. They each have a
> > >
> known number of interacting
parts. But the nature of the
> > >
> interactions is perhaps limits how ontologies in the usual
> > >
> sense can be used. The limitation is that ontologies are based
> > >
> in discrete mathematics.
> >
>
> > >
Pat Hayes replied
> >
>
> > >
??? No they aren't. Where did you
get this odd notion from?
> > >
PatH
>
>
> > By
which I mean such as set theory, algebra, combinatorics, logic,
etc.
>
>
> > --
Jeff
>
> OK. But set
theory is not particularly discrete. Sets are the basis for all
mathematics,
> including
continuous mathematics. Similarly, logic is not particularly concerned with
> discrete
structures: one can use logics to describe the continuum. (There is a
> technical
issue in that purely first-order logic cannot completely characterize the
>
finite/infinite distinction and hence cannot fully describe continuity; but then
pure
> FOL cannot
fully characterize finitude, either.)
> On the
other hand, ontologies don't seem to have any obvious
connection
> with combinatorics or algebra.
>
>
PatH
OK, not
“algebra,” but “algebras.” I have
in mind, for example, functions and similar transformational mappings,
topological spaces, and similar structures that are sometimes brought up in
discussions of ontological structures.
Surely
combinatorics and ontologies both involve graph theory, a branch of discrete
mathematics. Combinatorics, with the theory of algorithms (another discrete
mathematics) is used in ontology applications such as data mining and knowledge
bases.
I certainly
understand that logics are used in describing the continuum, and have a place in
real analysis.
Recall that the
original query from Andreas Tolk was the application of ontologies in systems
engineering. I pointed out that systems engineering has quite a bit to do with
complexity and hierarchy, part of the continuous
mathematics.
Consider also
the useful threads previously that discussed time as an ontology element. This,
too, suggests that a continuous component does not easily fit into a generally
accepted method of ontology development involving concepts and instantiations of
concepts.
My experience in
extremely large systems development has taught me that the hierarchy of systems,
subsystems, and primitives is too often minimized, leading to failures during
development and deployment.
--
Jeff