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Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG, IKL and the re

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 15 Jan 2008 18:05:39 -0500
Message-id: <478D3C43.50302@xxxxxxxxxxx>
Pat,    (01)

I am glad that you like Graeme Hirst's note about contexts,
because I also agree with him.    (02)

But the following is not my position:    (03)

> So let us return to the McCarthy/Sowa claim that 'contexts
> are whatever satisfy the axioms of our theory of contexts',
> and ask what the general theory of contexts *is*, and we
> find that it isn't anything.    (04)

As I have said, the only coherent notion is the syntactic one.
And a related syntactic notion appears in the literature of
linguistics and comp. sci. in the notion of a "context free"
vs. a "context sensitive" grammar.    (05)

A context-free grammar has rules of the following form:    (06)

    A -> B C D ...    (07)

A context-sensitive grammar has one or more rules of
the following form:    (08)

    x A y -> x B C D ... y    (09)

where x and y are arbitrary strings that specify the
"context" that is required as a prerequisite for using
this rule.    (010)

Other methods for specifying the "context" of a
"context sensitive" grammar include putting extra
information in a symbol table or other structure.    (011)

But all of them involve some mechanism for specifying
the additional information somewhere, even though the
methods for using that information may be very different.    (012)

So that is all I was proposing:  some conventions for
specifying two kinds of information:    (013)

  1. An identifiable (by name, for example) package containing
     a proposition (or conjunction of propositions) that specify
     the "context" for something x (also identifiable).    (014)

  2. A set of axioms that specify something about the information
     in the package and its relationship to x and to anything
     else (i.e., whatever might be considered "relevant").    (015)

That is *not* a general theory of context.  It is a syntactic
mechanism that makes it possible to state a specific theory
of context.  For example, if somebody says    (016)

     Bob promised Sue that p.    (017)

The context would contain the statement of p, it would be
related to Bob, Sue, and the act of promising, and there
would be some axioms for the verb 'promise' that would
specify the relationships.    (018)

This is very general, and I admit that it does not say very much.
But it provides a mechanism that makes it possible to formulate
theories that people have called "context theories".    (019)

John    (020)

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