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

To: Pat Hayes <phayes@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 18 Jan 2008 01:50:03 -0500
Message-id: <47904C1B.7000801@xxxxxxxxxxx>
Pat,    (01)

All of those issues you raise are certainly "relevant" to
somebody for some reason, which differs from case to case:    (02)

 > This 'something' might be what the text is, in some sense,
 > 'about', the thing or part of the world which defines its topic,
 > what the text is focused on; or it may be the overall 'background'
 > in which the text is situated. In the latter case, it isn't
 > necessarily what the text is actually about in any sense. So
 > for example, in the case of a time-interval, the text which is
 > "in" such a context might make no reference to times at all,
 > and yet still require that the reader know what time it is 'set'
 > in, in order to know that "the President" refers, say, to Jimmy
 > Carter.    (03)

That is why I agree *very strongly* with people like Graeme Hirst
and you, who claim that there is little or nothing that is common
to all uses of the word 'context'.    (04)

 > Maybe you mean to cover both of these by speaking of 'relevance'
 > but I wonder if its worth distinguishing them more exactly, as
 > they really do seem different, and maybe need different syntactic
 > treatment.    (05)

My definition is purely formal.  Any notion of aboutness or relevance
is not part of the formal definition.  Those issues are in the
"eye of the beholder", not in the definition.    (06)

To restate the point I was trying to make, there are three components
of the framework I am proposing:    (07)

  1. Central to any notion of 'context' is some "text", which may be
     expressed in any language, formal or informal.    (08)

  2. The references in that text refer to something x, which could
     be another text, but it could also be anything else of any type.
     I used the word 'situation' as an example, but x could just as
     well be a dog, as considered from the point of view of a flea.    (09)

  3. And finally, there must be some other text (axioms, for example),
     which state how #1 is related to #2.    (010)

None of the three components of this definition depend on the words
'relevance' or 'about' or 'purpose'.    (011)

If you prefer to see formal definitions expressed as n-tuples, I am
assuming a triple (T1,X,T2), where T1 is the some text stated by
sentences or expressions in some language L1, X is anything at all,
and T2 is more text stated in some language L2, which may or may not
be similar to the language L1.    (012)

If I were using IKL, I would translate T1 to IKL and put the result
in an IKL expression of the following form:    (013)

    (that translation-to-IKL(T1) )    (014)

I would refer to X by some suitable name or description that
would be related to the above that-expression by some suitable
dyadic relation.  And I would use the translated form of T2 as
an axiomatization of the relation that links T1 to X.    (015)

If you want an intuitive justification of my formal definition,
I would say that X is the "context" (in an informal sense) of
the text T1, and the axioms (formal or informal) in the text T2
"explain" how T1 and X are related to one another.    (016)

I claim that this formal definition (when suitably filled out
with appropriate instances of the triple (T1,X,T2) ) can capture
the essentials of various kinds of context theories within a
rather simple formal framework that is sufficiently general to
accommodate a wide range of positions.    (017)

John    (018)

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