ontolog-forum
[Top] [All Lists]

Re: [ontolog-forum] new logic

 To: "[ontolog-forum]" , "John F. Sowa" Rob Freeman Wed, 20 Jan 2010 20:59:31 +1300 <7616afbc1001192359j66a654ack629bccca2194e2e2@xxxxxxxxxxxxxx>
 ```On Wed, Jan 20, 2010 at 4:57 AM, John F. Sowa wrote: > ... > RF> Is it not true that a lot of what we might regard as >  > "meaningful" about some programs, such as whether they >  > will ever halt, will escape any such description? > > ... > > For some pairs of (M,T), the predicate Will_Halt can be > determined by a proof in FOL.  But for others, the theorem > prover will loop forever.  But any (M,T) that is undecidable > in FOL will be just as undecidable in English or any other > language, formal or informal.    (01) It may be enough to emphasize that point, i.e. that for some systems the only meaningful arbiter is the system itself (viewed as a computable process?) There is no more succinct "description".    (02) What I am always trying to draw people's attention to are the implications of this, or equivalent logical results, for meaning representation.    (03) I fully believe it will eventually prove possible to represent any meaning, completely, in the steps of a computable process. And I accept it will be possible for the steps of that computable process to be described in FOL, or any other formalism. What I think will not prove possible, what is demonstrated to be impossible in general, and what I think your use of the word "described" implied, for some, perhaps leading to confusion, is for the sum of the steps to be summarized in FOL. For that there may be no more succinct representation than the computable process itself.    (04) Your use of "described" is fair. I can see how you came to it. I just think it tended to hide this point: that FOL, any logic, anything, cannot in general summarize the totality of steps in a computable process.    (05) >From a knowledge representation point of view, if it turns out "meaning" can only be fully represented by computable processes, then there will indeed be something (Paola's "new logic"?) which cannot be captured by FOL: the sum of steps in a computable process.    (06) -Rob    (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 To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (08) ```
 Current Thread Re: [ontolog-forum] new logic, (continued) Re: [ontolog-forum] new logic, Patrick Cassidy Re: [ontolog-forum] new logic, Christopher Menzel Re: [ontolog-forum] new logic, Adrian Walker Re: [ontolog-forum] new logic, Christopher Menzel Re: [ontolog-forum] new logic, Patrick Cassidy Re: [ontolog-forum] new logic, Jakub Kotowski Re: [ontolog-forum] new logic, John F. Sowa Re: [ontolog-forum] new logic, Patrick Cassidy Re: [ontolog-forum] new logic, John F. Sowa Re: [ontolog-forum] new logic, Rich Cooper Re: [ontolog-forum] new logic, Rob Freeman <= Re: [ontolog-forum] new logic, Paola Di Maio Re: [ontolog-forum] new logic, John F. Sowa Re: [ontolog-forum] new logic, Paola Di Maio Re: [ontolog-forum] new logic, John F. Sowa Re: [ontolog-forum] new logic, ravi sharma Re: [ontolog-forum] new logic, Paola Di Maio Re: [ontolog-forum] new logic, Rick Murphy