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

 To: "[ontolog-forum]" Patrick Cassidy Thu, 30 Jun 2005 21:06:50 -0400 <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. >>> >> >>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) ```
 Current Thread Re: [ontolog-forum] Context, at last!, (continued) Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Duane Nickull Re: [ontolog-forum] Context, at last!, Duane Nickull Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Duane Nickull RE: [ontolog-forum] Context, at last!, Peter F Brown Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Nicolas F Rouquette Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Patrick Cassidy <= Re: [ontolog-forum] Context, at last!, Chris Menzel