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## Re: [ontolog-forum] Time representation

 To: "[ontolog-forum] " "Barker, Sean (UK)" Pat Hayes Thu, 24 Jan 2008 11:01:55 -0600
 At 10:23 AM +0000 1/24/08, Barker, Sean (UK) wrote: This mail is publicly posted to a distribution list as part of a process of public discussion, any automatically generated statements to the contrary non-withstanding. It is the opinion of the author, and does not represent an official company view. The problem with "points" is that one cannot exactly explicitly represent most points - or any non-rational number. Why does one need to explicitly represent (I think you mean numerically represent) something in order for it to be useful in one's ontology? One does not. A physics ontology might talk of atoms, even though they are too small to see and impossible to capture or name singly. And in any case, you are presuming that time is the real line. Maybe it isn't. Intuitive time doesn't seem to be. Computers make matters worse, as they only explicitly represent a small subset of the rationals. I did start looking at formalization of fuzzy edged intervals as part of a PhD in formal definitions of computational geometry, but when I realised I'd have to start by rewriting topology, I got on with my life. :-)  I almost went to graduate school to study topology. Fascinating subject. Fuzzy intervals aren't the way to go, IMO tolerance spaces are much more 'natural' and don't need real numbers. They also have a natural metric structure. The discussion reminds me of the story of a man looking for his keys by a street lamp. When asked where he had dropped them, he pointed to a place a little way off - "but the light is much better over here". Old story, but I fail to see the relevance. The, er, point of points is that they are useful. And, by the way, you can't not have them, in a sense. One can construct the points from the intervals. So in a sense they have to be there, whether you talk about them or not.   Sean Barker BAE SYSTEMS - Advanced Technology Centre Bristol, UK +44(0) 117 302 8184 BAE Systems (Operations) Limited Registered Office: Warwick House, PO Box 87, Farnborough Aerospace Centre, Farnborough, Hants, GU14 6YU, UK Registered in England & Wales No: 1996687   ________________________________   From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes       Sent: 22 January 2008 18:54      To: [ontolog-forum]      Subject: Re: [ontolog-forum] Time representation                         *** WARNING ***         This mail has originated outside your organization,      either from an external partner or the Global Internet. Keep this in mind if you answer this message.                    At 12:19 PM -0500 1/22/08, John F. Sowa wrote:           Pat,                             That statement is true of the standard model:                            > if you have intervals, you have the points at their ends.      Its true of all models, standard or not. One can mathematically construct the points from the intervals (they are maximal filters on the space of all meeting pairs of intervals.) See p 32 et. seq. of    http://www.ihmc.us/users/phayes/TimeCatalog.pdf         Suggestion:  use the word 'instant' instead of 'point': No, even instants have endpoints, and they may not be the same (though they can be: one gets very different meeting algebras in the two cases))              1. That allows instants to be infinitesimally small (i.e.,                   mathematical points).       Points are not quite the same as infinitesimally small intervals. Intuitively, the latter are the limits of intervals, but the former are the limits of places where intervals meet.                 2. But it leaves open the question of finite granularity.       Even in a discrete granularity model, there is a necessary distinction between (for example, assuming a 1-second grain) the point 02:13:01 and the moment (irreducible interval) 2:13:01-2:13:02. See section 3.4 (page 21) of http://www.ihmc.us/users/phayes/TimeCatalog.pdf, especially the discussion of 'models' on pp 23-4.     By the way, you have to be very careful when combining discreteness assumptions with 'limit' notions such as infinitesimal. I found that many apparently intuitive axioms about discreteness in fact have models in the real line when limits are allowed. See the discussion on page 44.           3. It also avoids the question of whether the grain is                      a sharply delimited interval or a distribution, such                      as a quantum mechanical wave packet that fades away                      without any sharply defined boundary.       Hah. Good luck with giving axioms for that model.                  4. It also leaves open the nature of an interval, which                      could be defined with instants at the ends that might                     themselves be have fuzzy boundaries.        Again, Ive never seen a coherent axiomatization of the idea of a fuzzy boundary. One related idea which is fully formalized is that of 'tolerance spaces', which are defined in terms of a "just-indistinguishable" relation on a set of points. That seems like a good approach to formalizing notions of approximation: but again, I have yet to see a fully worked-out ontology for this. And I wonder, in fact, if it is really necessary in order to do almost all practical temporal reasoning            By using the word 'instant', we can state generalizations                 that are true of a wide range of models without making a                 firm commitment to the nature of the granularity.        We can do that already: the 'catalog' has a very wide range of options. Nevertheless, it is always necessary to make at last a conceptual distinction between intervals and points, or else to face up to the sometimes unintuitive consequences of conflating them (see section 5 of the 'catalog'. I actually find this 'vector continuum' theory quite elegant and intuitive, but it certainly is not the traditional real line!)   Pat              John                                                     _________________________________________________________________                Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/            Subscribe/Config: 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 Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx                   --               ---------------------------------------------------------------------    IHMC               (850)434 8903 or (650)494 3973   home         40 South Alcaniz St.       (850)202 4416   office        Pensacola                 (850)202 4440   fax    FL 32502                     (850)291 0667    cell       phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes       ******************************************************************** This email and any attachments are confidential to the intended recipient and may also be privileged. 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 Current Thread Re: [ontolog-forum] Time representation, (continued) Re: [ontolog-forum] Time representation, matthew.west Re: [ontolog-forum] Time representation, Pat Hayes Re: [ontolog-forum] Time representation, Ian Bailey Re: [ontolog-forum] Time representation, Pat Hayes Re: [ontolog-forum] Time representation, John F. Sowa Re: [ontolog-forum] Time representation, Pat Hayes Re: [ontolog-forum] Time representation, Duane Nickull Re: [ontolog-forum] Time representation, Pat Hayes Re: [ontolog-forum] Time representation, Randall R Schulz Re: [ontolog-forum] Time representation, Barker, Sean (UK) Re: [ontolog-forum] Time representation, Pat Hayes <= Re: [ontolog-forum] Time representation, Barker, Sean (UK) Re: [ontolog-forum] Time representation, Pat Hayes Re: [ontolog-forum] Time representation, Barker, Sean (UK) Re: [ontolog-forum] Time representation, Barker, Sean (UK) Re: [ontolog-forum] Time representation, Jerry Hobbs Re: [ontolog-forum] Time representation, Duane Nickull Re: [ontolog-forum] Time representation, matthew.west Re: [ontolog-forum] Time representation, John F. Sowa Re: [ontolog-forum] Time representation, Ed Barkmeyer Re: [ontolog-forum] Time representation, Ed Barkmeyer