I have been "loosely" using context as an argument in a
"holdsInContext" relation, which gives propositions of the form:
(holdsInContext ?Prop ?Context) (01)
. . . and a proposition that holds in one context does not
necessarily hold in another. (02)
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). (03)
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? (04)
260 Industrial Way West
Eatontown NJ 07724
> -----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'
> 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
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