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Re: [ontolog-forum] Ontological Means for Systems Engineering

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Schiffel, Jeffrey A" <jeffrey.a.schiffel@xxxxxxxxxx>
Date: Mon, 26 Jan 2009 12:21:13 -0600
Message-id: <ECF42862FCA16D41BFA98F8C45F0955405723C85@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>

> > > > 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


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