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)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (013)
|