Chris --
Is there any particular theory of context that you find especially
convincing? (01)
Pat (02)
Chris Menzel wrote: (03)
> On Fri, Jun 17, 2005 at 12:26:04PM -0700, Duane Nickull wrote:
>
>>Chris Menzel wrote:
>>
>>
>>>ID: if x = y, then anything true of x is true of y.
>>>
>>
>>Disagree.
>
>
> Well, we haven't really fixed the context rigorously enough for there to
> be anything to disagree about. In the context of standard first-order
> logic with its usual extensional semantics, the above principle is
> rendered schematically as follows:
>
> For any well-formed formula A not containing the variable y, the
> following is an axiom:
>
> ID_FOL: x = y -> (A -> A'),
>
> where A' is the result of replacing every free occurrence of x in A
> with an occurrence of y.
>
> And the fact is that, on the standard, extensional semantics for
> first-order logic, every instance of ID_FOL is valid. That's not
> something about which one can rationally disagree; it's just a
> mathematical fact about first-order languages and their models.
>
> What one might disagree with is that the principle ID (properly
> formalized) is valid in every logical context. And that is exactly what
> the counterexamples I mentioned were designed to show -- ID fails, or at
> least appears to fail, in contexts involving belief and necessity (among
> others).
>
>
>>Most things may be the same but it is still instance y as opposed to
>>instance x, therefore his axiom has a logic error.
>
>
> You lost me there, I'm afraid.
>
>
>>They are still two different things. It may be better to state:
>>
>>if x = y, then x is y and both should be called x.
>
>
> That rather seriously confuses the *value* of the variable "x" with "x"
> itself. It also seems implausible -- Mark Twain is Sam Clemens, but I
> don't see any particular reason why he *should* be called by either
> handle. (And aside from these points, the development of theories that
> include semantical notions like "called" are fraught with difficulty.)
>
>
>>Also - an important consideration of context is perceiver.
>
>
> Yes, that can be important. That is one reason there is a lot of active
> research on formal theories of context at the moment.
>
>
>>To you and I, a coffee table is a solid item, to a neutrino, it is a
>>lot of open space interspersed with a few bits of solid matter...
>
>
> True enough, so a neutrino's ontology of your front room will probably
> look a lot different than your front room ontology! Note, though, that
> the notion of context is often just assumed in the background of an
> ontology -- we often create ontologies *from the perspective of a given
> perceiver or set of perceivers*, e.g., domain experts in a mfg shop
> floor. For these cases, the notion of context needn't play an explicit
> role. More and more, though, we have a need to represent multiple
> ontologies arising out of different contexts within a *single*
> framework, and this requires explicit mechanisms that enable us to group
> pieces of information according to context -- and that's exactly what
> formal theories of context are attempting to provide.
>
> Cheers!
>
> Chris Menzel
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Subscribe/Unsubscribe/Config:
>http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>
> (04)
--
=============================================
Patrick Cassidy (05)
MICRA, Inc. || (908) 561-3416
735 Belvidere Ave. || (908) 668-5252 (if no answer above)
Plainfield, NJ 07062-2054 (06)
internet: cassidy@xxxxxxxxx
=============================================
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Unsubscribe/Config:
http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (07)
|