a simple definition of theory

Tom Gruber <Gruber@Sumex-AIM.Stanford.edu>
Message-id: <2923940656-1606455@KSL-Mac-69>
Date: Thu, 27 Aug 92  14:44:16 PDT
From: Tom Gruber <Gruber@Sumex-AIM.Stanford.edu>
To: srkb@ISI.EDU
Subject: a simple definition of theory
It seems that I introduced some confusion by waffling on the
definition of the word "theory" in the context of logic and
definitions.  Here is a definition that seems to be consist with
standard usage and the recommendations of people I've asked who are
authorities on such matters:

   A theory is a set of sentences.   (Sentences = axioms.)

We can leave open whether a set of definitions is anything else than a
run-of-the-mill set of sentences.  Same for contexts viz theories.
Would that suit the needs of this discussion?

In my comments about contexts, all I meant was that I would leave it
to McCarthy, Guha, and company to distinguish contexts from ordinary
theories.  I was raised to believe that a theory is a set of

--- Excerpt from Charles Petrie (Thu, 20 Aug 92 14:07:02 MET DST) ---

> (By "theory", I mean the set of valid inferences in the traditional
> computer science sense, not Guha's "contexts".)
> For example, when I sent you my description of REDUX', it included a set
> of concepts and a theory, in standard PC, about the relationships
> between those concepts.

--- Excerpt from John McCarthy (Fri, 21 Aug 92 23:50:22 -0700) ---

> Quine made the term technical, saying that the ontology of a theory is
> the correspondence between variables in the theory and the domains
> in which they take their values.  Roughly then, the ontology of a theory
> is given by the kinds of things assumed to exist over which the
> variables can range.  This usage is also more appropriate for computer
> science than the fuzziness of current computer science usage.

--- Excerpt from Tom Gruber (Mon, 24 Aug 92  16:20:08 PDT) ---

> I reserve the technical term "theory" for the folks who are working
> out the important and subtle distinctions needed to handle contexts
> (microtheories, etc).  Second, whether there is a distinction between a
> set of definitions and an arbitrary set of axioms (which is one of the
> formal definitions of "theory") is a longstanding, interesting, and
> currently popular RESEARCH QUESTION in the knowledge representation
> community.

--- Excerpt from Charles Petrie (Tue, 25 Aug 92 11:42:07 MET DST) ---

> But I'm not ready to surrender the perfectly good technical term
> "theory" to folks working on contexts.  There is a formal definition of it
> for computer science, and it's in the textbooks.  I will continue to use it
> to mean a set of axioms (and their closure if I remember from Nilson),
> which may include object definitions.

--- Excerpt from phayes@herodotus.cs.uiuc.edu (Thu, 27 Aug 1992 13:01:31 -0600) ---

> The usage of 'theory' to mean a set of sentences is very
> well-established in logic.  The distinctions between different kinds of
> sentential role - eg.  'defining axiom' and 'conservative definition' - is
> more recent, but that usage of 'theory' is nailed down now.