Re: Response to George Ferguson

From: George Ferguson (
Date: 05/02/02

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    patrick hayes wrote:
    > 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.
    Surely intervals not having interiors is only more intuitive to those 
    whose intuition has been honed by years of familiarity with the 
    mathematics of infinite series and limits (themselves not the most 
    intuitive concepts--think how long it took for mathematicians to figure 
    them out).
    > 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 (?)
    Our proposal involved the *additional* stipulation (axiom) to the effect 
    that all intervals are proper. We have no problem with that not being in 
    the core ontology, provided we can add it consistently to our extension. 
    Ditto properties not (necessarily) holding at points.

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