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## Re: [ontolog-forum] Truth

 To: "[ontolog-forum] " Pat Hayes Sat, 7 Jul 2012 10:39:57 -0500 <97025659-81F5-4029-A65D-512AE3C7BAE3@xxxxxxx>
 ```Small correction below:    (01) On Jul 7, 2012, at 9:51 AM, Pat Hayes wrote:    (02) > > On Jul 7, 2012, at 9:39 AM, Michael Brunnbauer wrote: > >> >> Hello Chris, >> >> On Fri, Jul 06, 2012 at 01:08:57PM -0500, Chris Menzel wrote: >>>> So someone trying to define OWL FOL would have to be careful to stay in >>>> first >>>> order logic because Properties are first class entities ? Would that be a >>>> difficult problem ? >>> As long as one adds no special semantic requirement that there must be as >>> many properties as there are sets of individuals (which, by Cantor's >>> Theorem, is simply impossible to require if properties are "first-class >>> entities", i.e., a species of individual), there is no risk of moving >>> beyond first-order logic. >> >> After some reading, I think I begin to understand this. As long as the >> properties I can quantify over are first class entities, I have Henkin >> semantics. Only if I can quantify over all possible properties, I get true >> second order logic. >> > > Exactly. It all turns on what assumptions the semantic makes about what >higher-order entities (functions, relations) must exist. Classical second >order logic assumes that all mathematically possible functions and relations >exist. Henkin semantics assumes that all lambda-definable entities exist. >Common Logic makes no existence assumptions at all other than that names must >denote things with relational extensions.    (03) Actually, that all *terms* must denote things with extensions. So if you use functions, that use does carry some consequences for the number of entities in the universe.    (04) Pat    (05) > > So here is a case which distinguishes CL from Henkin. Do > > (P a) > (Q b) > > together entail > > (exists x)(and (x a)(x b) )) > > ? > > CL says no. Henkin says yes: the relevant function is (lambda (y) (or (P y)(Q >y))). > > Pat > >> Regards, >> >> Michael Brunnbauer >> >> -- >> ++ Michael Brunnbauer >> ++ netEstate GmbH >> ++ Geisenhausener Straße 11a >> ++ 81379 München >> ++ Tel +49 89 32 19 77 80 >> ++ Fax +49 89 32 19 77 89 >> ++ E-Mail brunni@xxxxxxxxxxxx >> ++ http://www.netestate.de/ >> ++ >> ++ Sitz: München, HRB Nr.142452 (Handelsregister B München) >> ++ USt-IdNr. DE221033342 >> ++ Geschäftsführer: Michael Brunnbauer, Franz Brunnbauer >> ++ Prokurist: Dipl. Kfm. (Univ.) Markus Hendel >> >> _________________________________________________________________ >> 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 >> >> > > ------------------------------------------------------------ > IHMC (850)434 8903 or (650)494 3973 > 40 South Alcaniz St. (850)202 4416 office > Pensacola (850)202 4440 fax > FL 32502 (850)291 0667 mobile > phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes > > > > > > > _________________________________________________________________ > 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 > >    (06) ------------------------------------------------------------ IHMC (850)434 8903 or (650)494 3973 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 mobile phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes    (07) _________________________________________________________________ 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    (08) ```
 Current Thread Re: [ontolog-forum] Truth, (continued) Re: [ontolog-forum] Truth, Chris Mungall Re: [ontolog-forum] Truth (Tim B-L's vision for the SW in 2000), John F Sowa Re: [ontolog-forum] Truth (Tim B-L's vision for the SW in 2000), William Frank Re: [ontolog-forum] Truth (Tim B-L's vision for the SW in 2000), John F Sowa Re: [ontolog-forum] Truth (Tim B-L's vision for the SW in 2000), John Bottoms Re: [ontolog-forum] Truth, Kingsley Idehen Re: [ontolog-forum] Truth, Pat Hayes Re: [ontolog-forum] Truth, Chris Menzel Re: [ontolog-forum] Truth, Michael Brunnbauer Re: [ontolog-forum] Truth, Pat Hayes Re: [ontolog-forum] Truth, Pat Hayes <= Re: [ontolog-forum] Truth, Avril Styrman Re: [ontolog-forum] Truth, John F Sowa Re: [ontolog-forum] Truth, Avril Styrman Re: [ontolog-forum] Truth, John F Sowa