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## Re: [ontolog-forum] Foundation Ontology Primitives

 To: "[ontolog-forum]" Rob Freeman Mon, 8 Feb 2010 16:31:21 +1300 <7616afbc1002071931i4fed3bc3o4689ec2d52f1c285@xxxxxxxxxxxxxx>
 ```John,    (01) On Mon, Feb 8, 2010 at 10:30 AM, John F. Sowa wrote: > > RF> But we have to remember there are at least some properties >  > of computable processes which are not specified, other than by >  > running the process itself. > > That is no different from running a theorem prover on the axioms: > > If you have a program for which the halting problem is undecidable, > the program will loop forever. > > If you try to determine whether the program will halt by starting > with the axioms, your theorem prover will loop forever. > > That makes the two different specifications -- the axiomatic and > the procedural -- identical in meaning ...    (02) You can think of the axioms as specifying an answer, it's true. But what use is that "answer" if you will have no access to it until the theorem prover halts. If it always halted the difference would just be one of time. But if it may never halt?    (03) The actual non-halting case is only of theoretical interest. An infinitely looping program is not of much practical use.    (04) It becomes more interesting when a process does halt. Say, there may be specific conditions under which one or other axiom applies.    (05) What the halting "problem" tells us is that you cannot simply list these true and untrue cases. You might have to go on forever waiting to see if your process halts and you can add another case to your list.    (06) If the halting "problem" did not exist, it would be possible to list all the true axioms with some finite process and we would have our FO. That the halting "problem" does exist means the testing process may go on for ever, there is no finite process to get them all, and the best you can do is test the ones of interest to you as you come across them.    (07) However, on the plus side, given any case, you can run a process and if it halts you have an answer, the exact conditions for halting telling you the validity of your theory.    (08) So in practice you can get any answer which is possible. But only by running a process, and seeing if it halts.    (09) -Rob    (010) _________________________________________________________________ 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    (011) ```
 Current Thread Re: [ontolog-forum] 2D drawing primitives (was: Foundation Ontology Primitives), (continued) [ontolog-forum] Foundation Ontology primitives, FERENC KOVACS Re: [ontolog-forum] Foundation Ontology primitives, AzamatAbdoullaev Re: [ontolog-forum] Foundation Ontology primitives, Rich Cooper [ontolog-forum] Foundation Ontology Primitives, FERENC KOVACS [ontolog-forum] Foundation Ontology Primitives, FERENC KOVACS Re: [ontolog-forum] Foundation Ontology Primitives, David Eddy Re: [ontolog-forum] Foundation Ontology Primitives, John F. Sowa Re: [ontolog-forum] Foundation Ontology Primitives, Rob Freeman Re: [ontolog-forum] Foundation Ontology Primitives, John F. Sowa Re: [ontolog-forum] Foundation Ontology Primitives, Rob Freeman <= Re: [ontolog-forum] Foundation Ontology Primitives, Christopher Menzel [ontolog-forum] foundation ontology primitives, FERENC KOVACS Re: [ontolog-forum] foundation ontology primitives, Rich Cooper Re: [ontolog-forum] foundation ontology primitives, John F. Sowa Re: [ontolog-forum] foundation ontology primitives, Rich Cooper Re: [ontolog-forum] foundation ontology primitives, Rob Freeman [ontolog-forum] Foundation Ontology Primitives, FERENC KOVACS Re: [ontolog-forum] Foundation Ontology Primitives, Rich Cooper