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Re: [ontolog-forum] Context, at last!

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Patrick Cassidy <pcassidy@xxxxxxxxxxxxxxxx>
Date: Thu, 30 Jun 2005 21:06:50 -0400
Message-id: <42C4972A.9040906@xxxxxxxxxxxxxxxx>
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. 
> 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
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>     (04)

Patrick Cassidy    (05)

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