Re: CCAT: TIME: All is well (Pat Hayes)
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Date: Wed, 9 Nov 1994 14:52:01 -0600
To: (Fritz Lehmann),,
From: (Pat Hayes)
Subject: Re: CCAT: TIME: All is well
Cc:, anquetil@IRO.UMontreal.CA,,,, billrich@VNET.IBM.COM,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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At  8:39 AM 11/9/94 -0600, Fritz Lehmann wrote:
..a long message about time and other things, including....

>     I'd like to see a preliminary draft of Pat Hayes' TIME ontology as soon as
>possible.  Since it includes a notion of clocks, it may span several of the
>above core subjects.

I have finished this for now, it is a collection of overlapping collections
of axioms and definitions written in KIF, together with a text discussing
it, all in the form of a Word file. I would be happy to send it to anyone
who wants it. It is not a single theory, but an attempt at a survey of
several of the axiomatic treatments of time that have been proposed.
Whether this an "ontology" or not I leave others to decide, but if it isnt,
then I am willing to cooperate with anyone who can help make it into one. 
We were having some problems with Ontolingua because it doesnt seem to fit
into Ontolingua's format for definitions.

>     Bernard Moulin also indicated a need for a "Lap" - a specified gap or
>time between intervals, expressed in seconds, days etc.,

In my account(s), this would be a duration. Durations measure quantitity of
time, intervals are pieces of time, points are (more or less) places in

 as well well as a
>REPEAT for iterativity (repetitive situations), NEVER and ALWAYS.  I'm
>confident that these can be provided by the TIME ontology. 

 As Daniel Bobrow
>pointed out, many of these notions, like "every third tuesday in 1962" can be
>defined on formal discrete math objects to which times correspond, rather
>than directly on time itself.  Once we have some sort of time-line, the
>apparatus of sets and intervals can be used (real, rational or discrete,
>depending on choice of time-line).  As Bobrow said, "we need a theory of
>selection from ordered sets, and notions of exceptions."\

Yes....except, one qualification. Sometimes, intervals CANT be regarded as
sets of points.
>     Pat Hayes answered Bobrow:
>-------begin HAYES quote-----
>     The answer is: you certainly can create variants of interval algebras
>and interval orders in which the primitives are discontinuous, and no doubt
>many a nice doctorate will be obtained from their study.  For CCAT ontology
>purposes, though, I don't think it "repays further effort", especially since
>I am presuming that we will have the math and logic available to
>painstakingly describe any particular discontinuous interval in terms of its
>continuous components

We may not be communicating here. There are two questions: whether time is
continuous or not; and what kinds of interval (eg intermittent) might be
worth looking at carefully. I presume you mean "disconnected" components.
>     David Whitten pointed out Cyc's ECTIs ("Easily Conceptualized Time
>Intervals") which are a limited, useful set of intervals and interval

Where are these published?

 I suggest we adopt and name these in CCAT with the Cyc names
>where convenient, but define them in the CCAT TIME ontology (which I suspect
>will have the rationals as the default basis of the number line, right, Pat?)

No. The rationals are one model, but several time (actually, line) theories
(Eg Allens) dont fit naturally onto the rationals in the usual way.
>..............rer.   For approximate time intervals,
>the Rome ontology just provides tolerances for the beginning and end points
>of an interval (like plus-or-minus fifteen minutes).

Oh, THAT is easy. But that doesnt realy get to grips with the difficult
problems. TO see why they might be hard, consider that these ends (15
minutes before and after) are themselves, presumably, subject to
imprecision, and that this process is infinitely, or arbitrarily,

I agree that this is probably not a reason to not have useful, quick ideas
like this available, but it does mean that thre is more work to be done in
this elusive area of imprecision and tolerancing.

One of the theories in the collection treats intervals as approximations to
points, by the way, but it is rather a weak theory.

>     Pat Hayes and Bernard Moulin discussed indexicality and time.  This
>should not be cause for worry. 

Im not so sanguine, but we will see.
>     I'm slightly troubled by the use of the precise MEETS relation as the
>time primitive;

Using MEETS is exactly equivalent to assuming that points are totally
ordered. The precision that bothers you is implicit in the notion of a
point itself. However, there are ways to treat some points as being very
small intervals, and I develop this in the theory catalog.

By the way, Allen and I showed some time ago that all binary interval
relations can be defined in terms of MEETS (given some very plausible
assumptions about intervals), so if you have MEETS then the others are
almost certainly definable, whether or not you choose to call MEETS a

 it might be nicer to use a "robust" relation, one which is
>unaffected by minuscule perturbations, as the primitive. 

You can indeed use others, notably some which are disjunctions of a subset
of the Allen relations. However, the definitions of the "precise" relations
then turn out to be recursive in nightmarish ways, and cannot have the
semantic force that is intended (ie ther are always nonstandard models.) I
cant prove this, but I bet I can convince you of it over a beer.

 I think Martin
>Golumbic or somebody is studying this class of interval algebras (based on
>the appropriate robust subset of Allen's time relations). 

Id like to hear more about this, if anyone [TURN TO AUDIENCE] knows of a

Pat Hayes

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