John (01)
I'm glad to see you already breaking your own guidelines - I wasnt convinced
it was a very viable model to start with :-) From my point of view I'm
happy for you, and many others on this forum, to post many times a day if
you feel so inclined because your posts are always worth reading, and it
preserves individual threads (as you have done here - unlike me who has
hijacked this thread to comment on another!) rather than mashing them
together. The underlying issues about conduct here, as others have noted,
are mutual respect and keeping a sanity check that a topic doesnt stray too
far off the stated core agendas of this forum, which I interpret to be
related but several and not confined just to repositories. I would be happy
for Peter (Yim) to occasionally be a little more proactive in suggesting
that certain threads are off topic; perhaps that happens off line in any
case. (02)
Godfrey (03)
----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Thursday, January 28, 2010 2:01 PM
Subject: Re: [ontolog-forum] Fw: Context in a sentence (04)
>
> Ali,
>
> I'm violating my one-note-per-day recommendation because I wanted
> to address the following point:
>
> AH> The theories / ontologies in COLORE do not constitute one single
> > giant lattice.
>
> Of course not, because the lattice is infinite. It represents all
> *possible* theories that can be stated in any given logic. I use
> the term 'hierarchy' for that subset of *currently defined* theories
> that happen to be stored in any given repository.
>
> AH> Unless I have misunderstood, whereas the lattice mentioned in
> > your work consists of a single relation "logical extension,"
> > there are multiple links in COLORE: specifically representation
> > theorems / definable interpretations etc.
>
> In my KR book, I adopted the three basic operators of the AGM
> axioms for theory revision: expansion, contraction, and revision.
> Then I added a fourth operator of analogy. As a brief summary
> of the four operators, see Figure 4 of the following paper:
>
> http://www.jfsowa.com/pubs/dynonto.htm
> A Dynamic Theory of Ontology
>
> All possible operations for transforming or relating any two
> theories can be defined as combinations of those four operators.
> Actually, you only need three operators, since revision can be
> defined as a sequence of contractions and expansions. Analogy
> is the operator you can use for representation and interpretation.
>
> You can explain all methods of theory revision, learning,
> discovery, representation, and interpretation as methods
> of walking or jumping through the lattice. Expansion and
> contraction are single-step operators used in walking, and
> analogy introduces jumps.
>
> You can also use the lattice to explain the difference between
> monotonic and nonmonotonic reasoning. Classical deduction starts
> with some subset of a theory (called the axioms) and derives any
> or all of the propositions of the full theory. All versions of
> nonmonotonic reasoning explicitly or implicitly involve expansion
> or contraction that walk through the lattice to a theory that is
> different from the one you start with. Analogy is a high-speed
> method for relabeling predicates in order to convert (or relate)
> one consistent theory to another.
>
> Finally, the lattice is the foundation for modularity. Simple
> modules are located in upper areas of the lattice, and consistent
> combinations of modules are the infimum of the modules from which
> they were derived.
>
> I am *not* claiming that I discovered everything that could be
> discovered about relating theories. And I am certainly not
> claiming that I anticipated what you wrote in your book.
>
> The only point I'm making is that the lattice is a systematic
> framework for showing how all the methods that have been invented
> or could ever be invented are interrelated.
>
> John
>
>
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> (05)
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