|From:||William Frank <williamf.frank@xxxxxxxxx>|
|Date:||Thu, 8 Mar 2012 15:04:31 -0500|
On Thu, Mar 8, 2012 at 1:32 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
Am Mar 8, 2012 um 6:23 PM schrieb William Frank:
Actually, I was making something up to save words, that seemed clear, indeed only theories can be consistent or otherwise, two models are inconsistent if there are two theories of which they are models, which are inconsistent.
Well, what I had in mind is ontologies for things like trade services or pharmaceuticals. These seem alot more complex to me than geometry etc. As many in these exchanges have noted, most large software collections are probably inconsistent, but consistency is to be hoped for. To expect one of them to be complete is a stretch, and probably not desireable.
> (only theories as bounded and richly expressed as second order arithmetic tend to be complete),
Sorry, I was not clear. There are two meanings of complete floating around. I was using semantic completeness, in the model theory semantically complete sense, as used by Baldwin "what is a complete theory?"
A (consistent) theory T in a logic L is complete if for every
T |= L
T |= ¬ L.
where the sideways sleepy |= means logically follows from, not is provable from.
As opposed to the completeness of a proof theory, which means as you say, if it follows, then you can prove it.
The term "completeness," as it applies to a logic, I believe, is only as you define it. As it applies to a contentful theory expressed in a logic, I believe it usually means what I an Baldwin mean.
Second order arithmetic is sematincally complete while it is proof theoretically incomplete, since second order logic itself is proof-theory incomplete.
you are right, that might be an easier way to say it, especially if you expand out all my lazy ellipses. Or else completely (no pun intended) on the model theoretic side. Mixing the two together is generally a more complex thought to follow.
The point remains, which was the point of the mail: ontologies do not guarantee complete "interoperability", but that term probably needs and does not have a definition. And if ontologies only guarantee something partial, what is it that they DO guarantee? And why, in practice, do even primitive but logical shared messaging specifications like the early tagged syntax S.W.I.F.T provide so much value, and not seem to lead us into trouble. (While some shared but literally insane messaging specification like the health care EDI messages create huge error and correspondingly huge employment opportunities
This email is confidential and proprietary, intended for its addressees only.
It may not be distributed to non-addressees, nor its contents divulged,
without the permission of the sender.
_________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (01)
|<Prev in Thread]||Current Thread||[Next in Thread>|
|Previous by Date:||Re: [ontolog-forum] Constructs, primitives, terms, Patrick Cassidy|
|Next by Date:||Re: [ontolog-forum] Constructs, primitives, terms, Matthew West|
|Previous by Thread:||Re: [ontolog-forum] Constructs, primitives, terms, Christopher Menzel|
|Next by Thread:||Re: [ontolog-forum] Constructs, primitives, terms, Matthew West|
|Indexes:||[Date] [Thread] [Top] [All Lists]|