Re: CCAT: TIME: Fantasyland?/Various issues (Pat Hayes)
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Date: Wed, 19 Oct 1994 14:24:09 -0600
To: Danny Bobrow <>,,
        Fritz Lehmann <>
From: (Pat Hayes)
Subject: Re: CCAT: TIME: Fantasyland?/Various issues
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At  9:12 AM 10/18/94 -0700, Danny Bobrow wrote:
>It seems that the concepts  such as every last Friday of every third
>month are not concepts of time, but concepts that derive from our
>ability to count, select and name. I can ask for every tallest student
>from every third classroom, etc.  Once we have chunks, and names for
>chunks of time (MTWHFSS, or Jan Feb, or 1884) and an ordering among
>names, then we can use our ability to compose selection functions on
>ordered sets   The fact that some calendar programs select some of these
>is "just" user convenience (no small matter if you want to sell).  So we
>need a theory of selection from ordered sets, and notions of exceptions.

I think this is both right and maybe wrong. (This is the logician speaking,
remember ;-) Right because these concepts are surely definable in terms of
simple temporal notions like 'interval' and 'duration' and then a suitably
powerful way of describing sets of things and integers and so on, and the
process is going to be very like defining the tallest student from every
classroom, etc.  All a clock is, is a starting time and an 'beat' interval
which it keeps on counting, for example. In fact there are some generally
useful ideas that can be defined very abstractly, such as the sequence of
n'th things from a sequence of sequences, etc.; there might be a useful
general-purpose theory of counting and selecting.

However....there are some tantalising possibilities. For example, the
thirteen simple-interval relations which James Allen described form a
complete algebra, and this algebraic perspective turns out to be a useful
and productive way to think about them. Suppose we allow intermittent
intervals: is there a collection of relations on them which has the same
kind of role that the Allen relations plays for simple intervals, ie is
there a useful algebra of relations-between-intermittent-intervals? People
have looked at this but I dont know of a definite answer. The questions go
beyond whether we *can* describe this stuff (answer, yes) to whether it
repays further effort to see if it can be described in other ways. And the
answer to THAT question, in my view, is whether the results from it (ie the
'theory' of intermittent intervals) are likely to be of any use to anyone.
Thats what Im trying to discover by pestering the world through the

And theres another slight qualification. Im *pretty sure* that most
temporal ideas can be described in terms of simple ones like point,
interval and duration plus general-purpose ideas like the n'th in a
sequence. But Im never going to be *entirely certain*, and so its always
worth actually trying to do it, just to keep testing the basic time
theories. You never know when a flaw might show up.


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