[SCL] Interesting find

[Robert E. Kent]

Bill,

One approach to this is to follow the idea of John Sowa and others, that
there will be many, many, many domain ontologies and that quite a few of
these will need to work with such mathematical and generic theories. Hence,
it makes sense to have a standard generic meta ontology for binary relations
and order-theoretic structures. This is the approach of the Information Flow
Framework (IFF), where binary relations and order theories are currently
housed (and somewhat scattered) in the IFF Upper Core (meta) Ontology
(IFF-UCO)
http://suo.ieee.org/IFF/metalevel/upper/ontology/core/version20020102.pdf
where "antisymmetric", "transitive" and "closure" are axiomatized on pages
57 and 58, the IFF Lower Core (meta) Ontology (IFF-LCO)
http://suo.ieee.org/IFF/metalevel/lower/ontology/core/version20020515.pdf,
and the IFF lower core Set namespace (IFF-SET)
http://suo.ieee.org/IFF/metalevel/lower/namespace/set/version20030402.pdf.
To borrow a phrase from the SCL working document, the IFF aims to be " a
general framework that exists to define [meta-semantic and] meta-syntactic
mappings on a principled basis, [hopefully] in a way that allows reasoning
agents to draw appropriate conclusions."

Robert E. Kent
rekent at ontologos.org

----- Original Message -----
From: "Bill Andersen" <andersen at ontologyworks.com>
To: "SCL List" <scl at philebus.tamu.edu>
Sent: Friday, March 12, 2004 4:23 PM
Subject: [SCL] Interesting find


> Folks,
>
> I don't know what the plans are for support of function- and
> relation-denoting functions, but I ran across an interesting case where
> such would be needed:
>
> Say you want to talk about the notion of membership in an organization.
>   Call the relation 'member'.
>
> So you would want to allow:
>
> member(a,b)
> member(b,c)
>
> But not
>
> member(a,a)
> member(b,b)
> member(c,c)
> member(b,a)
> member(c,a)
> member(c,b)
>
> It's certain that member is asymmetric, but its transitive closure is
> as well.  I'd like to be able to
> say something like:
>
> asymmetric(transitiveClosureOf(member))
>
> without having to explicitly introduce a relation into my ontology that
> is the transitive closure
> of member.
>
>     .bill
>
> --
> Bill Andersen (andersen at ontologyworks.com)
> Chief Scientist
> Ontology Works, Inc. (www.ontologyworks.com)
> 1132 Annapolis Road, Suite 104,
> Odenton, MD 21113
> Office: 410-674-7600
> Cell: 443-858-6444
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>
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