Preserving cross-context truths cannot only be specified, the
construction also has to also be shown. A formal manner for drawing
and documenting the architecture of context is missing. (01)
Deborah L. MacPherson
Specifier, WDG Architecture PLLC
Projects Director, Accuracy&Aesthetics (04)
On 4/16/07, Cassidy, Patrick J. <pcassidy@xxxxxxxxx> wrote:
> John, PatH:
> I have been "loosely" using context as an argument in a
> "holdsInContext" relation, which gives propositions of the form:
> (holdsInContext ?Prop ?Context)
> . . . and a proposition that holds in one context does not
> necessarily hold in another.
> This is somewhat off the topic of whether an identifier means the same
> thing in different contexts (I prefer that they do, and use
> context/namespace prefixes to address clashes).
> But I am very concerned about what can be stated about the preservation
> of truth between contexts.
> For example, if a "context" is a time interval in the real world, what
> is true in one time interval may not be true in another. However, some
> things tend to remain true for long periods of time, such as the
> location of Mount Rushmore; and other things tend to remain true in
> every spatial context (e.g. the number of protons in an oxygen
> nucleus). Has there been any discussion of how to address
> cross-context preservation of truth in a formal manner?
> Patrick Cassidy
> 260 Industrial Way West
> Eatontown NJ 07724
> Eatontown: 732-578-6340
> Cell: 908-565-4053
> > -----Original Message-----
> > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> > John F. Sowa
> > Sent: Monday, April 16, 2007 10:41 PM
> > To: [ontolog-forum]
> > Subject: Re: [ontolog-forum] Ontology,Information Models and
> > the 'Real World'
> > Pat,
> > I sympathize with your attitude toward much of the loose talk
> > about contexts:
> > > ... 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.
> > I'm happy with that.
> > > 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.
> > 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.
> > They way I represent talk about a dog or a flea or the kitchen sink
> > as a context is straightforward:
> > 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.
> > 2. Then I use the "that" operator of IKL to represent the context
> > box and its nested CGs as a proposition p.
> > 3. Finally, I use a *description* relation (Dscr) to link #1 and
> > #2 by Dscr(x,p).
> > 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
> > John
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