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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 16 Jan 2008 12:06:29 -0600
Message-id: <p06230902c3b3f3659a1a@[]>
At 6:05 PM -0500 1/15/08, John F. Sowa wrote:

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

But the following is not my position:

> 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.

As I have said, the only coherent notion is the syntactic one.

Oh come, that is too strong. I don't think all the other notions are incoherent. I just think they have virtually nothing in common.

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.

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

    A -> B C D ...

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

    x A y -> x B C D ... y

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

Well, thanks for muddying the water even further, I didn't think that was possible :-) This seems to be yet another notion of 'context'.

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

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.

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

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

Just say, a way to name propositions. Yes, we need that. But the idea of a proposition being a "context" of something isn't needed anywhere, as far as I can tell. In the McCarthy/Guha logic, its the other way round: the proposition is itself true "in" a context.

  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").

That is *not* a general theory of context.  It is a syntactic
mechanism that makes it possible to state a specific theory
of context.

How can there be a theory of things that nobody can say what they are?? Or on which everyone disagrees about what they are? What use is such a theory, when it is not required for either conceptual or linguistic analysis, and when all the logics that have been devised to describe it are less expressive than a non-contextual logic?

  For example, if somebody says

     Bob promised Sue that p.

The context

WHAT context? That is a perfectly ordinary English sentence, and it refers to Bill, Sue, promising, and a proposition or sentence p. It does not mention contexts and it does not need any reference to contexts in order to be parsed or analyzed. Why do you them immediately start talking about contexts?

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.

The logical analysis of this sentence is that a promising relation holds between Bob, Sue and a sentence or proposition, the content of the promise. Or maybe a bunch of relations between an act of promising and Bob, Sue and a sentence or proposition. But I don't see any place in there for anything that anyone would call a 'context', or any need to even mention contexts.

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".

I'll only be interested in such theories when I actually see one. I havn't seen one yet, in spite of over a decade of metatheory and philosophizing about the general topic, five workshops, dozens of technical papers, at least 4 formal logics, etc. etc..



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