SUO: Re: *Date 15 Apr 2002 -- Theory Query
Jon,
Yes, as I have commented in several places, see for example the discussion
of truth concept lattices and 1st-order interpretations in the second half
of the message
http://grouper.ieee.org/groups/suo/email/msg05960.html,
--------------------
we are dealing with a _fibered structure_ here. I have proposed that the
truth concept lattice be used in SUO as John Sowa's potentially infinite
open-ended lattice of theories. However, there is no single lattice here but
an infinite collection of lattices, where each truth classification
"truth-classification(L)" and each truth concept lattice "truth-lattice(L)"
is based upon (indexed by) a particular 1st-order language L.
--------------------
The IFF Upper-level Classification Ontology
<http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf>
can handle these truth classifications and truth concept lattices, when they
can be specified. The IFF Model Theory Ontology (IFF-MT)
<coming your way in a few weeks>
will provide terminology for specifying these truth classifications and
truth concept lattices. As I mentioned in a previous message today, the
notion of a knowledge base as discussed in the Conceptual Graphs Standard
http://users.bestweb.net/~sowa/cg/cgstandw.htm .
can be input as an IFF-MT model, and these models incorporate a 1st-order
language consisting of type labels, relation labels and coreference labels.
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: "Jon Awbrey" <jawbrey@oakland.edu>
To: "SUO" <standard-upper-ontology@ieee.org>; "SemioCom"
<gdsemiocom@univ-perp.fr>; "CG" <cg@cs.uah.edu>
Sent: Sunday, April 14, 2002 10:11 PM
Subject: SUO: *Date 15 Apr 2002 -- Theory Query
>
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
> SUO WG Members,
>
> With special reference to those speculating
> about sundry "lattices of theories" (LOT's):
>
> What is your definition of a "theory"?
>
> More acutely to the purpose:
>
> What is a theory that it should latticed be?
>
> I have asked this question many times before,
> and all I've gotten is lots of gesticulation.
>
> In particular, I am skeptical that you can even find,
> without begging the question of intercommunicability,
> any definition of a lattice of theories that remains
> invariant over the choice of a language in which the
> theories are expressed, indeed, where the finding of
> the envisioned common language of comparison is just
> another way of stating the initial problem to be met.
>
> Consider this standard definition of a theory, the only one I know,
> such as makes sense within the favored frame of first-order logics:
>
> | A '(first-order) theory' T of $L$ is a collection of sentences of $L$.
> |
> | T is said to be 'closed' iff it is closed under the |= relation. Etc.
> |
> | Chang & Keisler, 'Model Theory', page 36.
>
> Notice that the very definition of a theory is stated
> relative to a given first-order predicate language $L$.
> Until such a common language has been established, all
> talk of lattices or other orders is just so much Babel.
>
> Jon Awbrey
>
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>