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## Re: [ontolog-forum] Terminology and Knowledge Engineering

 To: "[ontolog-forum] " Michael Brunnbauer Wed, 25 Jan 2012 00:48:09 +0100 <20120124234809.GA14338@xxxxxxxxxxxx>
 ``` Hallo Rich,    (01) some explanations, as I discovered that what I wrote is not Gödels first incompleteness theorem but something that follows easily for first order theories:    (02) > On Tue, Jan 24, 2012 at 12:34:19PM -0800, Rich Cooper wrote: > > Gödel showed that any logical system at least as > > powerful as arithmetic is necessarily conflicted; > > there are true theorems that cannot be proven and > > there are false theorems that cannot be refuted.    (03) This is the first incompleteness theorem: There will always be a theorem A that cannot be proven and it's negation not A also cannot be proven.    (04) As you can model arithmetic with a first order theory, Gödels completeness theorem would be valid with such a theory. This means that if A and not A cannot be proven, they also not entailed by the theory. This means the negation of these statements:    (05) Every model of the theory is a model of A Every model of the theory is a model of not A    (06) Which is equivalent to:    (07) There is a model of the theory that is not a model of A (where A is false) There is a model of the theory that is a model of A (where A is true)    (08) > Gödel showed that there are always theorems that are independent of such a > system. That is: They are neither true or false because there are models > of the system where they are true and there are models where they are false. > A model is an interpretation of all symbols of the system where all > restrictions/axioms are true. The system is "ambiguous".    (09) Regards,    (010) Michael Brunnbauer    (011) -- ++ 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    (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] Terminology and Knowledge Engineering, (continued) Re: [ontolog-forum] Terminology and Knowledge Engineering, Michael Brunnbauer Re: [ontolog-forum] Terminology and Knowledge Engineering, David Eddy Re: [ontolog-forum] Terminology and Knowledge Engineering, Dave McComb Re: [ontolog-forum] Terminology and Knowledge Engineering, Dave McComb Re: [ontolog-forum] Terminology and Knowledge Engineering, Rich Cooper Re: [ontolog-forum] Terminology and Knowledge Engineering, Michael Brunnbauer Re: [ontolog-forum] Terminology and Knowledge Engineering, Rich Cooper Re: [ontolog-forum] Terminology and Knowledge Engineering, Michael Brunnbauer Re: [ontolog-forum] Terminology and Knowledge Engineering, Rich Cooper Re: [ontolog-forum] Terminology and Knowledge Engineering, Michael Brunnbauer Re: [ontolog-forum] Terminology and Knowledge Engineering, Michael Brunnbauer <= Re: [ontolog-forum] Terminology and Knowledge Engineering, Christopher Menzel Re: [ontolog-forum] Terminology and Knowledge Engineering, Rich Cooper Re: [ontolog-forum] Terminology and Knowledge Engineering, Christopher Menzel Re: [ontolog-forum] Terminology and Knowledge Engineering, John F. Sowa Re: [ontolog-forum] Terminology and Knowledge Engineering, Pat Hayes Re: [ontolog-forum] Terminology and Knowledge Engineering, Christopher Menzel Re: [ontolog-forum] Terminology and Knowledge Engineering, Rich Cooper Re: [ontolog-forum] Terminology and Knowledge Engineering, John F. Sowa Re: [ontolog-forum] Terminology and Knowledge Engineering, Pat Hayes Re: [ontolog-forum] Terminology and Knowledge Engineering, Pat Hayes