# Re: Response to George Ferguson

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