On Fri, Dec 16, 2005 at 10:53:03AM -0700, Paul S Prueitt wrote:
> On Fri, Dec 16, 2005 at 08:22:20AM -0700, Paul S Prueitt wrote:
> > > In this case, the concept of "infinite" must be a potential but not
> > > actual computational structure.
> > [Menzel:]
> > The mathematical framework of the modern theory of computation -- as
> > well as the semantics of RDF(S) and OWL -- is classical, in which
> > there is no notion of a potential infinite.
>
> <Comment by Paul Prueitt>
> Many of us are pointing out that there is no mathematical framework
> for computation ... (01)
*stunned silence* (02)
> - at least not an axiomatic foundation like one sees
> in abstract algebra, topology, number theory, real analysis etc... (03)
You're very badly mistaken there. Recursion theory -- the foundation of
modern computer science -- was developed as an axiomatic theory pretty
much from the beginning, notably in the form of Church's lambda
calculus. That (among other sources) evolved into the field of
combinatory logic, which, in addition to providing a framework for
recursion theory, serves as a foundation for functional programming.
Recursion theory can also be axiomatized in a more familiar way in the
language of second-order Peano Arithmetic and is in fact derivable in a
first-order form in Zermelo-Fraenkel set theory. For the former, see S.
Simpson, Subsystems of Second-Order Arithmetic (Spring, 1999). For the
latter, any comprehensive text on set theory. (04)
> Let me state this differently, trying to anticipate the polemic that
> Chris will enjoy setting up. (05)
Polemic? There's nothing to debate here. These are just mathematical
facts. (06)
> Any "mathematical framework" (what ever "this" might mean") (07)
Surely this is not problematic. A mathematical framework is simply the
background mathematical theory one uses for establishing the
mathematical foundations of some area of research, e.g., first-order
Zermelo-Fraenkel set theory. (08)
> proposed for computational theory, can be replaced with a different
> framework any time the object of the theory is altered. (09)
This makes no clear sense. (010)
> Pure computer science thus has a problem with relevance. John is
> talking about this when he mentions that if computer science omits the
> importance of human reality, then we have an issue of relevance. (011)
Human reality is no more relevant to theoretical computer science than
it is to quantum electrodynamics. Of course, there are issues of
usability in applied CS -- interface issues, human factors, intellectual
property issues, etc, but those have nothing to do with the points at
issue. (012)
> One also finds no single mathematical framework for modern physics, as
> seen in the results of Godel and the incomplete status of physics. (013)
The relevance of Gödel to modern physics is questionable, but be that as
it may, the mathematical foundations of modern physics have nothing to
do with the rather straightforward issues I was addressing. (014)
> Roger Penrose's book, as John Sowa has been pointing out, is an
> excellent "complete" overview of modern foundations to physical
> theory. (015)
And largely irrelevant to the construction of the vast majority of
ontologies that will prove useful to the Semantic Web. (016)
> > > I agree that the concept of infinite is a valuable one, but one
> > > that might be "merely" constructed by human ability to create
> > > (induce) abstract formal systems.
> >
> > It is hard to see what bearing this philosophical question has on the
> > engineering problem of creating and maintaining high-quality ontologies
> > and developing effective software for making use of them.
> >
> <Comment by Paul Prueitt>
> The point that is made over and over again, is that only part of the
> task of creating ontology is within the confines of "engineering".
> [Equivalent statement is: the field of biology cannot be reduced to
> the field of engineering]. (017)
True enough, but who would be silly enough to think that? (018)
> > > 2) Semantic dimension is complex: If RDF is seen as being
> > > sufficient only within a specific boundary (such as in dealing
> > > with simple relationships between data elements, then how does one
> > > address the semantic dimension when humans are interacting in a
> > > crisis - for example.)
> >
> > Your question seems, at least in part, to concern the expressive
> > limitations of RDF, so I'll address that. When RDF is too weak for you
> > to be able to say what you want, you use a more expressive language,
> > some variant of OWL being the obvious choice. OWL itself (by design)
> > has significant expressive limitations and hence might require further
> > supplementation by the likes of RuleML if more expressive power still is
> > needed. The new W3C Rules working group has been formed to (among other
> > things) bring some order to the problem of adding expressive power in a
> > principled way when OWL is not enough.
> >
> <Comment by Paul Prueitt>
>
> and why is OWL the obvious choice? (019)
It is obvious only in the sense that it is the natural first place to
look if one needs expressivity beyond RDF, since (a) it, like RDF, is a
W3C product and (b) it uses RDF syntax and was designed (in part)
expressly to extend RDF's expressive power. But as I already noted, it
too might well fall short of one's expressive needs. (020)
> The term "expressive" is where we (others) have a problem with what
> you are saying, Chris. You and others in the RDF/OWL camp. (021)
I'm in no such camp. RDF and OWL are useful tools for certain tasks and
useless or inappropriate for others. (022)
> (There is nothing "personal" here.) The term "expressive" is used to
> imply an ability to "express" the ontological reality what ever it may
> be. (023)
No, it isn't, at least not by me in this context. "Expressive power" is
a mathematically well-understood property of logical languages. It
bears no formal connection whatever to the informal idea of "expressing
ontological reality" (whatever that's supposed to mean). (024)
> But this ability has not been demonstrated in any systems that depend
> on or are similar to the W3C standards. The failure to be
> "expressive" is found in any example of "degeneracy" (the word as
> Edelman uses it) in the process mapping between structure and function
> - say specific to metabolic expression or gene expression. After the
> fact, one can specify to some degree or accuracy an ontology
> description of the pathway over the degeneracy. But before the fact,
> the W3C standard does not have any anchor to address the structural
> indeterminacy. (025)
Whether it does or not is an idle assertion until you formalize the such
concepts as "degeneracy" and "structural indeterminacy" and demonstrate
that the (formal) expressive resources of OWL are inadequate. They may
well be, but until your assertions are expressed rigorously, you've
provided no reason to believe that this is so. (026)
> I am not saying that W3C is a complete failure, or that there is no
> value or lessons learned that can be earned because of the past ten
> years of W3C dominance. I am saying what others are saying, that it
> is time to understand the limitations and move on. (027)
You have provided no rigorous demonstration of the limitations, so what
you are saying is idle chatter until you provide one. And as I've
already noted, W3C itself recognizes the expressive limitations of OWL.
This has led to the development of RuleML and SWRL, and is also a driver
behind the newly formed Rule Interchange Format group
(http://www.w3.org/2005/rules). (028)
> > > 3) The separation of the ontology concepts from first order logic
> > > specification: How first order logics might be separated from
> > > existing OWL programs and systems IN SUCH A WAY that the logic
> > > can be recombined easily.
> >
> > OWL is a declarative language for writing ontologies. There's no such
> > thing as an OWL program within the OWL spec. Also, OWL is based on a
> > language that is significantly weaker than that of full first-order
> > logic. As for "separating" the underlying logic from an OWL ontology
> > (?) and "recombining" them, you provide no account of what this might
> > mean, so it is impossible to answer your question.
>
> <Comment by Paul Prueitt>
> Look, and I appeal to others here. By OWL program, I meant a computer
> program written to depend on the OIL in OWL. (029)
OIL was also a declarative framework -- OWL is its successor to
DAML+OIL. But whatever; I was simply taking your statement at face
value. You talked about OWL programs. There's no such thing. (030)
> The attempt, Chris's attempt, here is to suggest that I somehow do not
> know what OWL is, and this is both unfair and unproductive. I
> understand this as part of a polemic, but I am willing to take the
> time to address point by point elements of a discussion. But this
> polemic just leads into personal insults. (031)
Dude, do you always impute dark and conspiratorial motives to those who
correct your mistakes? You said something false. Even if you *meant*
something completely sensible by it, in a public forum falsehoods need
to be corrected lest they generate further errors that hinder discussion
and progress. It is not about *you*. (032)
> It should be clear that I am suggesting to the working group that the
> task to be proposed might be precisely to
>
> "separate" the underlying logic from an OWL ontology and
> "recombining" them (033)
Until you make clear formal sense of "separate" and "recombine", there
is simply no well-defined scientific problem to address here. (034)
> Chris has actually created, and done a good job of it, a polemic that
> ridicules the notion that the logical apparatus often build into OWL
> ...can be removed . (035)
No, once again, I am simply pointing out that, until you clarify the
notion of "remove" (same as "separate"??), the claim has no meaning. (036)
> The reason why it should be removable is so that the concept
> relationships can be more easily edited and viewed by non-computer
> scientists. (037)
It sounds like all you are talking about is whether one can isolate the
non-reserved vocabulary in an OWL ontology. Of course that can be
"removed" for editing and viewing. Is *that* all you mean? (038)
> In the SUMO there is a separate "ontology concepts". The ontology
> concepts of SUMO can be extracted and written as RDF/XML without any
> of those parts of the SUMO that is separate from the minimal
> specification of the concept. <end of comment>
>
> > Cheers!
>
> <Comment by Paul Prueitt> I find very little to cheer about over this
> mess that you make when I (and others) try to engage on issues that I
> feel, and that others feel, are important IF there is to be usable
> standard beyond the impasse that your type of thinking seems to enjoy.
> It may be fun for some, but it is not fun for me.<end of comment> (039)
Good grief, don't take yourself so seriously. (040)
Chee^H^H^H^HRegards, (041)
Chris Menzel (042)
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