**From:** patrick hayes (*phayes@ai.uwf.edu*)

**Date:** 05/02/02

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>Below are some responses to George Ferguson's comments on the time >ontology. I should have a rewrite out tomorrow. > >If anyone on this mailing list doesn't want to be on it, please just >say so and I'll remove you. I promise not to sell your email address >to a Viagra marketeer in retaliation. (Now I've just lost everyone >who filters out messages mentioning Viagra.) > >-- Jerry > > > >> -------------------------------------------------------------------------- >> Overall, we like this initial formulation. It manages to capture >> generalities without excluding different people's theories. We tested >> the common ontology by seeing whether we could extend it with >> additional axioms to produce the Interval Temporal Logic as described >> in (Allen, 1984) and (allen & Hayes, 1989). This seems like a good >> exercise not only because it is near and dear to our hearts, but also >> because it's a widely-used and extensivley studied representation of >> time. >> >> Our comments in this note are divided into three sections: the first >> addresses issues in the development of the temporal logic through >> Section 2, the second notes a few fairly minor points that we came >> across in later sections of the proposal, and, finally, we describe >> our mapping or extension of the proposed logic into the Allen ITL. >> >> -------------------------------------------------------------------------- >> Comments on Temporal Logic: >> >> 1. INTERVAL-BETWEEN ought more properly to be called >> TEMPORAL-ENTITY-BETWEEN, given the definition near the end of 2.1. > >Sounds reasonable. How about TIME-BETWEEN? > >> 2. Near the end of 2.1, you comment that "the ontology is silent about >> whether intervals are uniquely determined by their starts and >> ends." That is, INTERVAL-EQUALS is not (necessarily) true equality. >> While this is certainly mathematically possible, it is different >> from the standard use of equality in the interval algebra (which >> uses only true equality). Also, in later examples you describe >> intervals as, for example "[10:00, 11:00]". We suspect that most >> people would expect that, for example, "Raining([10:00, 11:00])" >> and "~Raining([10:00, 11:00])" was logically inconsistent, although >> this would not necessarily be the case if intervals are not >> uniquely determined by their endpoints. So we are in the camp that >> would like to strengthen this. > >I have rewritten the treatment to make explicit this property and >where it is required. I also compare it with Total Ordering and >Convexity. On David Israel's suggestion I called it Extensional >Collapse, but if you have a better name for it I would be happy to use >it. It would be better to call it Intensional Collapse, which in any case would be a good thing to promote, as a general philosophical position to promote ontological well-being. Seriously though, I think we need to keep two things distinct: an ontology of the time-line, and an ontology for dealing with alternative ways that things might happen. I would like to keep these as orthogonal as possible. In a purely temporal ontology, the endpoints of an interval should uniquely define the interval (in fact, I would suggest that we *identify* intervals with pairs of endpoints in a basic temporal ontology.) > > 3. In 2.3 on the interval relations, it would appear that several of >> the definitions are counter-intuitive They seem counterintuitive if your intuition has been honed by years of familiarity with the Allen algebra, but they are in fact quite intuitive as a natural limiting case. I would prefer to say that the Allen reasoners make an implicit assumption which is itself slightly counterintuitve, that all intervals must have an interior. >unless restricted to proper >> intervals (those not of the form "[t,t]"). For example, a >> degenerate interval [t,t] INT-EQUALS itself, INT-MEETS itself, and >> is INT-MET-BY itself! Right, which is, to repeat, not only intuitive but also obvious. >Thus "Meets(X,Y) <-> ~MetBy(X,Y)" is not a >> theorem of these axioms. In fact, unless restricted to proper >> intervals, none of the standard antonyms of the interval algebra >> are theorems. True; they need to be generalized to cover the full space of possibilities. >And of particular interest in planning (cf. Allen & > > Koomen 1987), the degenerate interval is INT-DISJOINT from itself. > >It sounds like there are enough problems trying to keep the interval >calculus open to length-0 intervals that one should just stipulate >that the intervals have to be proper. I would suggest not doing that. Certainly proper intervals are a category worth having, and that fact that the Allen-style reasoners only work on them is worth bearing in mind; but it is also worth keeping the convention that the limiting case of a zero-length interval is indeed naturally regarded as being an interval. Why not just say that [t,t] is both a point and an interval (of zero duration), and that therefore t=[t,t] ? I think that this works just fine. Then not being the same as ones own endpoint(s) is a defining criterion for a proper 'fat' interval, as opposed to a point-like interval. Then every 'piece' of time is an interval (determined uniquely by its endpoints, which are totally ordered.) Maybe this is just a terminological distinction (?) Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes

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