Re: Response to George Ferguson

From: patrick hayes (
Date: 05/02/02

  • Next message: George Ferguson: "Re: Response to George Ferguson"
    >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 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 (?)
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