>On Mar 8, 2007, at 5:01 PM, Pat Hayes wrote:
>> ...The notion of
>> 'completeness' of a logic or inference machine is
>> well-established in logic, used in virtually all
>> textbooks, and has a clear, simple definition. It
>> means that if X is a logical theorem then a proof
>> of X exists, so that a complete inference engine
>> is one which will, in principle, find a proof of
>> X.
>
>Just a quick clarification to Pat's lucid post: Pat is using
>somewhat nonstandard terminology here, as the term "logical theorem"
>is usually used to refer to the provable sentences of a logical
>system. So understood, that would render Pat's definition trivial
>(which is obviously not what he had in mind). (01)
I say at least three trivial things before
breakfast, to get my brain into gear for the day. (02)
> The more common term
>in the definition of completeness is "logical truth", that is, a
>sentence that is true simply in virtue of the meanings of its
>component logical operators (or in logician-speak, true under all
>interpretations of its nonlogical vocabulary). (03)
Yes, sorry I was careless. Better still, I should
have said, if X is entailed then...,but in this
forum I was worried that we might get into a long
discussion of what 'entail' means :-) (04)
>
>Also, the completeness theorem is often stated in a somewhat more
>general form whose relevance to formal ontology is a bit clearer: A
>logical system (or inference machine) is complete if, for any set of
>sentences S (notably, the axioms of an ontology), if S logically
>implies X (that is, if X is true under any interpretation that makes
>all the members of S true), then there is a proof of X from S. (05)
Better, yes. Thanks. (06)
Pat (07)
>
>-chris
>
>
>_________________________________________________________________
>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
> (08)
--
---------------------------------------------------------------------
IHMC (850)434 8903 or (650)494 3973 home
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 cell
phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes (09)
_________________________________________________________________
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 (010)
|