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Re: [ontolog-forum] Ontology, Information Models and the 'Real World'

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 16 Apr 2007 22:40:36 -0400
Message-id: <462433A4.90704@xxxxxxxxxxx>
Pat,    (01)

I sympathize with your attitude toward much of the loose talk
about contexts:    (02)

> ... But in normal assertional logic, the quantifiers are the
 > only such name-binding operators. Of course all these languages
 > can be rendered down into functors applied to a single binder,
 > usually lambda.    (03)

I'm happy with that.    (04)

> BUt contexts in context logic play a rather different role: in 
> particular, there is no explicit name binding syntax, only the notion 
> that a name may (or may not) denote differently when asserted 
> relative to a context. Contextual assertion is more like inclusion 
> inside a modal operator than being in a syntactic binding scope.    (05)

I prefer very simple formal definitions:  a "concept" is a node
in a conceptual graph, and a "context" is a box into which you put
such graphs.    (06)

They way I represent talk about a dog or a flea or the kitchen sink
as a context is straightforward:    (07)

  1. I use the binding mechanism (such as the existential quantifier)
     to represent the thing that is called a context (dog, flea, or
     sink) by a variable x.    (08)

  2. Then I use the "that" operator of IKL to represent the context
     box and its nested CGs as a proposition p.    (09)

  3. Finally, I use a *description* relation (Dscr) to link #1 and
     #2 by Dscr(x,p).    (010)

I have never seen any theory of contexts with a coherent set of
axioms that cannot be represented (with a considerable increase
in clarity) by restating the axioms by the above method (possibly
with some additional relations and types, such as Situation or World).    (011)

John    (012)

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