Re: [CL] The Decidability Fetish
Dear Professor Lawvere,
One working definition for "ontology" as used by engineers might go as
follows: "An ontology is a formal, explicit specification of a shared
conceptualization. It is an abstract model of some phenomena in the world,
explicitly represented as concepts, relationships and constraints, which is
machine-readable and incorporates the consensual knowledge of some
community."
* [Semantic conceptualization:] Since it is "an abstract model of some
phenomena in the world" it is a semantic conceptualization.
* [Logic-oriented:] Since it involves "concepts, relationships and
constraints" it is logic oriented.
* [Formal and explicit:] Since it is "machine-readable" it is formal and
explicit.
* [Shared and relative:] Since it "incorporates the consensual knowledge of
some community" it is shared and relative.
All four of these characteristics of ontologies are represented in the
SUO-IFF project http://suo.ieee.org/IFF/, which is developing a descriptive
category metatheory for ontologies. In the IFF we distinguish between
populated and unpopulated ontologies. Unpopulated ontologies have only type
information [aka schemas or theories]. Populated ontologies have both type
and instance information, plus the classification relationship between these
two kinds of things [aka databases or local logics].
To be logic independent, the IFF represents and manipulates ontological
structures within the metatheory of institutions
http://www.cs.ucsd.edu/users/goguen/projs/inst.html. The IFF has
work-in-progress axiomatizations for (amongst others) the institutions of
information flow (IF), equational logic (EQL), order-sorted first order
logic (FOL) and simple common logic (SCL), and is developing an
axiomatization for the metatheory of institutions itself.
John Sowa's "lattice of theories" concept allows ontologies to be shared and
relative. Within the IFF representation, the lattice of theories is the
fibering or indexing of the context of theories by the context of signatures
(aka languages) -- all definable within institutions. Semantic integration
of ontologies can be represented by (1) aligning ontologies within a diagram
of theories and (2) fusing aligned ontologies via the colimit of a diagram
of theories.
Best wishes,
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: <wlawvere@buffalo.edu>
To: "John F. Sowa" <sowa@bestweb.net>; "Robert E. Kent"
<rekent@ontologos.org>
Cc: "Michel Eytan" <eytan@UMB.U-STRASBG.FR>; "SUO"
<standard-upper-ontology@ieee.org>
Sent: Tuesday, October 12, 2004 11:34 AM
Subject: Re: [CL] The Decidability Fetish
[snip]
I know that engineers seem to be
giving a more practical meaning to another term which philosophers use to
distract us under a deceptively simple "definition", namely "ontology".
Thus if I am indeed missing something I would appreciate an indication.
[snip]
Thanks again for giving me this window into the activities of the IEEE. Any
additional enlightenment will be gratefully received.
Sincerely, Bill Lawvere