ontolog-forum
[Top] [All Lists]

## Re: [ontolog-forum] Truth

 To: "[ontolog-forum] " , Michael Brunnbauer Pat Hayes Sat, 7 Jul 2012 09:51:58 -0500 <43B1EBAD-DCDB-4CEA-9369-3B7487C8E2D3@xxxxxxx>
 ``` On Jul 7, 2012, at 9:39 AM, Michael Brunnbauer wrote:    (01) > > 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. >    (02) 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) So here is a case which distinguishes CL from Henkin. Do    (04) (P a) (Q b)    (05) together entail    (06) (exists x)(and (x a)(x b) ))    (07) ?    (08) CL says no. Henkin says yes: the relevant function is (lambda (y) (or (P y)(Q y))).    (09) Pat    (010) > 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 > >    (011) ------------------------------------------------------------ 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    (012) _________________________________________________________________ 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    (013) ```
 Current Thread Re: [ontolog-forum] Truth, (continued) Re: [ontolog-forum] Truth, John F Sowa 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