ONT Re: Analytic Differential Ontology (ADO)
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John Velman wrote:
>
> It seems to me that the mention of differential forms
> in this context is a trope rather than an element
> of an analogy. But I'd certainly be interested
> to find out if I'm missing something.
>
> On the other hand, the program to understanding the
> relationships and transformations between ontologies
> is interesting. Perhaps category theory is the field
> on which this battle should be fought.
>
> John Velman
>
> Jon Awbrey <jawbrey@oakland.edu>@ieee.org on 12/05/2000 07:56:08 PM
>
> Sent by: owner-ontology@ieee.org
>
> To: "Stand! Unfold! Ontology!" <ontology@ieee.org>
> cc: John F Sowa <sowa@bestweb.net>, Robert E Kent <rekent@ontologos.org>,
> Pat Hayes <phayes@ai.uwf.edu>, Douglas McDavid <mcdavid@us.ibm.com>,
> Matthew West <Matthew.R.West@IS.shell.com>
>
> Subject: ONT Analytic Differential Ontology (ADO)
>
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>
> FOOturists,
>
> Questions that have arisen lately, on the themes of development,
> differentiation, and diversity among our ontologies, not to mention
> disagreement, dispersion, and discord among our perspectives on them,
> lead me to replay this note that I sent to John Sowa early last summer,
> thematizing an approach that I have been endeavoring to develop, a little
> something that I like to think of as "analytic differential ontology" (ADO).
>
> > Subject: Ontology & Process
> > Date: Sun, 04 Jun 2000 14:30:33 -0400
> > From: Jon Awbrey <jawbrey@oakland.edu>
> > To: John F Sowa <sowa@bestweb.net>
> >
> > #%%THIS%%%#%%%IS%%%%#%%%NOT%%%#%%%%A%%%%#%%FRAME%%#
> >
> > To John Sowa:
> >
> > Recent mentions of "process ontology" on the CG-list
> > have brought me back to related questions that I have
> > been working on for some time, from a slightly different
> > perspective, perhaps. I am concerned with the questions
> > of "difference in ontology", or "differential ontology",
> > including as special studies the issues of diversity and
> > change in the ontologies that different observers adopt.
> > Some of these questions are:
> >
> > Is there a reasonable framework or a language for talking
> > about "the geometry of the space whose points are views",
> > including the working ontologies that go with each and
> > every observer's/interpreter's "point of view" (POV)?
> >
> > Can we put the "chiasmatic commutator" to work on the
> > issue of process ontology -- turning the question around,
> > from asking about the "ontology of process" to asking about
> > the "process of ontology" -- that is, asking what sorts of laws,
> > if any, govern the dynamics of change in people's ontologies,
> > in other words, in the conceptual frameworks that people use
> > to posit their various ontological hierarchies?
> >
> > My personal approach to these sorts of questions, since the
> > complexities of the overlaid and shifting meta-perspectives
> > are enough to overwhelm a person at first, has been to stake
> > out an initial base camp at that simplest level of ontology
> > and conceptual framework that I can imagine, without being
> > completely trivial, the world of "zeroth order logic",
> > propositional calculus, truth table semantics, venn diagrams,
> > in short, the "alpha" part of Peirce's Existential Graphs.
> >
> > This has certainly been a big enough bite to chew on for a while,
> > given the difficulties of the NP-complete satisfiability problems
> > that arise, but I have been able to devise an efficient and powerful
> > enough extension of Peirce's basic syntax, along with a workable enough
> > implementation of basic computational tools for using this representation,
> > that I have been able to begin contemplating the "differential extension"
> > of propositional calculus -- in fact, one of the surprises of the whole
> > development is that not a few of Peirce's original ideas almost seemed
> > to demand this sort of extension.
> >
> > ( Note: I think that the most general name for this in mathematics
> > | is the "De Rham Extension", and I have begun to look into this,
> > | but it is really just what you do when you add differential forms
> > | to analytic geometry. All in all, I am just exploiting the analogy
> > | betweeen Propositional Calculus, as a study of functions B^n -> B,
> > | and Real Analysis, as a study of functions R^n -> R, and asking:
> > | What is the proper form of differential and integral calculus that
> > | goes with Prop Calc (Sentential Logic)?
> > )
> >
> > I guess I could be taken as posing the thesis here
> > that one way to approach the problem of talking about
> > change and diversity in these logical, ontological, or
> > qualitative realms might just be to start by looking at
> > what worked in the more quantitative domains of analysis
> > and physics. Of course, it is not likely that everything
> > will turn out to be exactly the same, and one must be
> > willing to tolerate a number of surprises.
> >
> <...>
> >
> > Enough for now,
> >
> > Jon Awbrey
> >
> > #%%%%%%%%%#%%%%%%%%%#%%%%%%%%%#%%%%%%Jon#Awbrey%%%#
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John V,
No, I realize that I have a bent for the sporadically exotic variety
of "tropological deformation", but this particular line was spoken
with one of my more approximately linear faces.
If you just think of doing differential geometry in GF(2),
you would eventually re-create this subject for yourself.
The "characteristic 2" case, where 1 + 1 = 0, does create
a few surprises along the way, and the consequential facts
that 2 = O and that "+" = "-" will cause a lot of the usual
distinctions to collapse, and this does place a few obstacles
in the way of the more mindless pleasures of analogy-chasing,
but not every analogy has to be so totally unmindful to work.
And, yes, a glove-box full of category-theoretic maps
will pretty much "go with the territory", as they say,
in their all too abstractly nonsensical way.
This "add-vertex-ment" that I sent to the CG List recently
will serve to explain the current condition of this work:
> Subject: CG: Re: Conceptual Graphs for Representing Temporal Knowledge
> Date: Fri, 24 Nov 2000 12:00:53 -0500
> From: Jon Awbrey <jawbrey@oakland.edu>
> Reply-To: cg@cs.uah.edu
> To: Manikanti Sreedhar Reddy <manikanti@rediffmail.com>
> CC: Conceptual Graphs <cg@cs.uah.edu>,
> Stand Up Ontology <standard-upper-ontology@IEEE.org>
>
> manikanti sreedhar reddy wrote:
> >
> > I'm doing my Masters Project on Representing Temporal knowledge
> > using the Conceptual Graphs, I need the following informaiton:
> >
> > - is there any work done similar
> >
> > Can anyone plz. suggest the other projects (Web sites; URLs)
> >
> > Thanks in advance
> >
> > m.sreedhar reddy
> > M.Tech (Artificial Intelligence)
> > University of Hyderabad
> > Hyderabad
> > India
>
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> Dear Mr. Reddy,
>
> I have been developing a series of extensions of propositional logic
> that are based on the Alpha Level of Peirce's Logical Graphs and that
> are intended to serve as a "calculus of variations" for this beginning
> level of functional expressions and sentential theories. As a special
> application, this involves a suite of concepts for dealing with issues
> of change and diversity in propositional contexts, and these concepts
> are closely analogous to the ordinary ways that one would extend, say,
> analytic geometry to differential geometry.
>
> An initial exploration of these ideas is presented in
> my paper "Differential Logic & Dynamic Systems", which
> I would be happy to send you a copy of, if you wish to
> send me (off-list) a mailing address. I am sorry that
> I do not yet have an e-copy, as this was written up in
> 1994 in a different disk format, with a lot of graphics,
> for which I no longer have the proper conversion package.
>
> Earlier this year I had begun to exposit some of these ideas
> on the CG List. Altogether, this involves:
>
> 1. RefLog, the reflective extension of logical graphs,
> 2. DifLog, the differential extension of logical graphs,
> 3. HopLog, the higher order propositional extension(s).
>
> I did not get as far as step 2,
> but here are the links, anyway:
>
> http://www.virtual-earth.de/CG/cg-list/msg03351.html
> http://www.virtual-earth.de/CG/cg-list/msg03352.html
> http://www.virtual-earth.de/CG/cg-list/msg03353.html
> http://www.virtual-earth.de/CG/cg-list/msg03354.html
> http://www.virtual-earth.de/CG/cg-list/msg03376.html
> http://www.virtual-earth.de/CG/cg-list/msg03379.html
> http://www.virtual-earth.de/CG/cg-list/msg03381.html
>
> There is also some exposition of this on the SUO List,
> chiefly under the topic of "Zeroth Order Logic" (ZOL):
>
> http://ltsc.ieee.org/logs/suo/msg01406.html
> http://ltsc.ieee.org/logs/suo/msg01546.html
> http://ltsc.ieee.org/logs/suo/msg01561.html
> http://ltsc.ieee.org/logs/suo/msg01670.html
> http://ltsc.ieee.org/logs/suo/msg01966.html
> http://ltsc.ieee.org/logs/suo/msg01985.html
> http://ltsc.ieee.org/logs/suo/msg01988.html
>
> But I have not been able to get to 2nd base there either.
> I hope that you find some of this "worth a click" (WAC).
>
> Best Wishes,
>
> Jon Awbrey
>
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I am "getting around to" having this work enscounced as
a Technical Report at the Oakland University CSE Dept,
but until that actually happens, I could send you
a copy by snail mail.
Many Regards,
Jon Awbrey
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