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## Re: [ontolog-forum] borrowing terminology

 To: Christopher Menzel "[ontolog-forum] " Pat Hayes Fri, 9 Mar 2007 10:41:10 -0600
 ```>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) ```
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