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## Re: [ontolog-forum] Time representation

 To: "'[ontolog-forum] '" "Patrick Cassidy" Wed, 23 Jan 2008 13:10:45 -0500 <008301c85deb\$46506230\$d2f12690\$@com>
 ```PatH, Thanks for the answer. The implementation of Time that I would like to use is one that I couldn't find in the Time Catalog - though I may not have interpreted all of the axioms correctly. What I would like is a representation of Time as isomorphic to the real line with: (1) open, closed and semi-open intervals, all distinguishable and specified by their endpoints (whether or not the endpoint is included in the interval) (2) a time point as a subtype of a closed time interval, and identical to a closed interval of zero length. (3) two time intervals closed at the adjoining ends both overlap and meet (I think this is not permitted in Allen's algebra); Intervals that both overlap and meet must both be closed at the meeting ends and have a single time point as the overlap interval. (4) dividing a time interval at a point gives rise (depending on the dividing operation) to either (a) two time intervals, each having a closed end with the point of division (and conversely, joining two time intervals that meet at closed ends merges the common point, which is a single ordinary point); or (b) two intervals open at the point of division; or (c) one interval (the earlier one) open and one (the later one) closed at the point of division. Operations a and b can divide an interval into two equal parts, if the starting interval ends are both closed or both open. Operation c can equally divide a closed-open interval. (5) catenating two intervals both open at the joining end creates the point of juncture. (6) Two intervals open at the adjacent ends also meet if those ends are defined by a common point (7) time points are both 'part of' and 'contained in' time intervals. (8) the default time interval type (if defaults are needed) is one closed at the lower end and open at the upper end - (This type is used to specify AM or PM in a day). (9) Events that occur at a single time point imply a preceding interval open at that point, in which the event state differs from the state at (and for some interval after) that point. Though unrealistic for physical events, this can be used to specify socially defined events, such as someone becoming president at a particular time point.    (01) But I didn't see (and may have missed) a single theory that has all of those requirements in the time catalog. Is such a theory actually in the time catalog - or elsewhere? If not, is it somehow internally logically inconsistent?    (02) PatC    (03) Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 cassidy@xxxxxxxxx    (04) > -----Original Message----- > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum- > bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes > Sent: Wednesday, January 23, 2008 12:12 AM > To: [ontolog-forum] > Subject: Re: [ontolog-forum] Time representation > > At 11:31 PM -0500 1/22/08, Patrick Cassidy wrote: > >Just a question about one point (so to speak): > > > >> > >> Re PTim: I realize that calling an interval a point is > problematical. > >> But in anything that has to do with the physical world, there is no > >> way to specify a true point. Perhaps a better term would be "grain > >> in time", abbreviated "Grit". > >> > > > >Has anyone observed any problems of *logical consistency* in > classifying a > >point on a line as being identical to a closed interval of zero > length, with > >beginning and end points identical? > > I presume you mean, interval on the real line. > None: this is quite consistent. This model > (actually several versions of it) is discussed in > the 'time catalog'. But it does produce some > complications. For example, consider a ball > tossed into the air. At one point in its > trajectory, its vertical velocity is zero. If > this is a closed interval [b,b], then the > intervals of positive and negative vertical > velocity must be open (or semi-open) intervals > (a,b) and (b,c). Now, these intervals have the > same endpoint, so they apparently meet (in the > sense used by Allen's interval algebra). Yet > there is an interval *between* them, so they > apparently cannot meet. So this model seems to be > incompatible with the Allen algebra, which is a > major problem. The ontology called the 'vector > continuum' there takes this idea and develops it > axiomatically rather than presuming the real > line, and gives a temporal ontology which I think > is quite neat. But it has some apparent oddities, > eg it allows negative intervals (which turn out > to be quite useful.) And it isn't possible > (AFAIK) to interpret it in the real line. > > > Or are the 'point' and 'interval' > >classifications merely two different views of the same thing? > > Really, there is no simple answer to this > question. Try reading some of the options > described in the catalog. I think the various > intuitions are reasonably well explained there. > > PatH > > > > >PatC > > > >Patrick Cassidy > >MICRA, Inc. > >908-561-3416 > >cell: 908-565-4053 > >cassidy@xxxxxxxxx > > > >> -----Original Message----- > >> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum- > >> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa > >> Sent: Monday, January 21, 2008 12:48 PM > >> To: [ontolog-forum] > >> Subject: Re: [ontolog-forum] Time representation > >> > >> Pat, > >> > >> The position I most strongly advocate is not a specific ontology, > >> but a framework of conventions for organizing a multiplicity > >> of special cases (not necessarily consistent with one another), > >> making the implicit relationships explicit, and providing tools > >> and guidelines for mixing and matching. The lattice of theories > >> is an example. Robert Kent's IFF is a much more ambitious example. > >> > >> I would recommend a fairly simple framework for starters, since > >> there's a danger of freezing half-baked ideas before they're fully > >> baked. (RDF, for example, was hardly out of the oven before > >> Tim Bray tried, unsuccessfully, to pull it back in.) > >> > >> > Do you have any granularity axioms? That is one of the hardest > >> > ontological problems, in my experience. > >> > >> There are so many hard problems, it's hard to say which are harder. > >> But the idea of taking the least significant digit as the criterion > >> for implicit granularity is fairly common for experimental data > >> (unless some explicit margin of error is stated). > >> > >> Re PTim: I realize that calling an interval a point is > problematical. > >> But in anything that has to do with the physical world, there is no > >> way to specify a true point. Perhaps a better term would be "grain > >> in time", abbreviated "Grit". > >> > >> John > >> > >> PS re HTML email formats: Your note of 11:18 was in a readable > font > >> for Thunderbird, but your note of 11:37 appeared in a tiny, tiny > font. > >> I had to increase the font size by two steps to make it the same as > >> the previous note. But then the fonts for all other notes were too > >> big, and I had to decrease the default by two steps. > > > > >> At least each of your notes was entirely in one font size. I've > >> received some email in which each paragraph was in a progressively > >> smaller font. That's why I hate HTML email. > >> > >> > >> _________________________________________________________________ > >> 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 > >> > > > > > >_________________________________________________________________ > >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 > > > _________________________________________________________________ > 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 >    (05) _________________________________________________________________ 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    (06) ```
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