SUO: Re: Re: Building the hierarchy
John and others,
----- Original Message -----
From: "sowa" <sowa@bestweb.net>
To: "SUO" <standard-upper-ontology@ieee.org>; <cg@cs.uah.edu>
Sent: Saturday, May 17, 2003 8:59 AM
Subject: SUO: Re: Building the hierarchy
[snip]
> 5. Robert Kent pointed out the difference between a theory and an
> axiomatization of a theory. In logic, the word _theory_ is applied
> to the "deductive closure" or the complete set of implications of
> some axioms. Since two or more axiom sets might have the same
The IFF uses the term "theory" for any set of sentences (and actually
extends this to expressions, i.e., formulas), and uses the term "closed
theory" for theories that are deductively or semantically closed (every
consequence or semantically entailed expression of the theory is in the
theory). This accords with both the book _Model Theory_ by Chang and Keisler
and the book _Information Flow_ by Barwise and Seligman. We are most
concerned that we are aligned with Barwise and Keisler, since the first
order notions (FOL) in the IFF extend the information flow (IF) notions in
Barwise and Seligman in a very coherent way (a quadruple of coreflections).
In particular, in the IFF the FOL notion of a closed theory adjointly
corresponds to the IF notion of a regular IF theory. So where you (John S.)
use "axiom set" and "theory", the IFF uses "theory and "closed theory".
Perhaps these two synonym pairs could be booknoted for later reference.
Robert E. Kent
rekent@ontologos.org