SUO: Re: Language And Module Processing (LAMP)
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Robert,
My aim was to think up a near minimal example in which
the issue of lexicon and axiomset merging might arise,
to which one might apply the abstract notions that
you were mentioning. It is better if the example
is one that might arise in a natural application,
that is, generated independently of the paradigm
that is applied to it. All this abstract lattice
stuff sounds nice from a distance, but the idea of
mushing together something like OpenCyc and SUMO
is a little like interweaving lines of code from
Cobol and Fortran, so I think that there is a bit
to be proven that any of this stuff makes sense
in practice. A concrete, simple example would
be a great aid to exposition, and might just
engender a few surprises.
Now, I am still casting about for the right level of abstraction.
If we are ever going have anything sensible to say about problems
like intercommunicability and interoperability, then I don't think
that we can avoid a few of the facts of actual lingustic usage,
but of course we do not want to get lost in all the details
of actual linguistic usage.
I reverted to the classical notion of terms logics to avoid a number
of distractions. But a typical FO theory is going to have a fragment
consisting of monadic predicates that you could consider on its own.
And that seemed like a good place to start. Those of us who think of
models as the things about which statements and programs and theories
are true, some of which things may actually exist in the actual world,
would then think of those statements and programs and theories as
somehow denoting those things. So that is all I meant by that.
Now, I know that the extensional type of quotient is not what you
were talking about, but it just came up as I tried to think about
how a natural example of language and axiomset merging might arise.
It is one of the ways that we discover constraints in practice,
and if you are going to talk about theory formation for real,
rather than supposing it to be some kind of purely syntactic
or purely deductive process, then it will be necessary to
deal with it somehow or other, as it really happens, and
not just by prior prescription.
I actually had a more interesting example from the
computational learning theory literature in mind,
but it will take some working up to before I can
tell if it's the right sort of thing.
Jon Awbrey
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Robert E. Kent wrote:
>
> Jon,
>
> This reply is associated with and to a certain extent relies upon
> the more detailed discussion that I gave in this morning's message
> "Building the Hierarchy by Language and Module Processing"
>
> http://suo.ieee.org/email/msg09555.html
>
> The quotients formed in Information Flow use the notion of a *dual invariant*
> as defined by Barwise and Seligman in their book on "Information Flow". These
> correspond to the endorelations and quotients for IFF type languages and theories --
> see the IFF type language and IFF theory namespace documents for further information
> and the axiomatizations:
>
> http://suo.ieee.org/IFF/metalevel/lower/namespace/type-language/version20021205.pdf
> http://suo.ieee.org/IFF/metalevel/lower/namespace/theory/version20021205.pdf
>
> These invariants, endorelations and quotients are exact
> and not soft notions (neither rough nor fuzzy).
>
> The "term logics" and the examples below correspond to FOL languages that
> have only sorts (entity symbols), but no non-sort relation symbols and no
> function symbols. The instances represented in the symmetric difference of
> the extents of the vehicle_1 and vehicle_2 entity types are not permitted in
> the notions of a dual invariant and quotient in Information Flow or in the
> notions of an endorelation and quotient for IFF type languages and IFF
> theories. In IF and the IFF any two equivalenced types must have the same
> extent. I presume that that means that these follow the "denotative" or
> "extensional" type of quotient operation. I am interested in extending the
> IFF to fuzzy notions, and perhaps this is one place where that might occur.
>
> Robert E. Kent
> rekent@ontologos.org
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