From: Drew McDermott (drew.mcdermott@yale.edu)
Date: 04/02/03
[[ I'm sending this just to daml-time@daml.org. If that means someone
obvious is missing, let me know. ]]
Comments on Pat's comments:
I tend to agree with his comment that the time-aggregate stuff is much
too complex. I've been reviewing RFC 2445, the standard calendar-data
interchange format, on which the iCal ontology is based. (I think
they've changed the name from iCal to something else.) It has an ad
hoc notation for temporal aggregates that covers just about every
possible sort of repeating event. E.g.:
Every other week on Monday, Wednesday and Friday until December 24,
1997, starting on Tuesday, September 2, 1997:
DTSTART;TZID=US-Eastern:19970902T090000
RRULE:FREQ=WEEKLY;INTERVAL=2;UNTIL=19971224T000000Z;WKST=SU;
BYDAY=MO,WE,FR
==> (1997 9:00 AM EDT)September 2,3,5,15,17,19,29;October
1,3,13,15,17
(1997 9:00 AM EST)October 27,29,31;November 10,12,14,24,26,28;
December 8,10,12,22
(rfc2445, p. 119)
It seems to me we could shift this into predicate calculus without
much trouble:
(agg-subdivide
(agg-skip
2
(agg-cut
(aggregate weekly
(hrFn 9 (daFn 2
(monFn 9 (yrFn 1997 (common-era est))))))
(daFn 24 (monFn 12 (yrFn 1997 (common-era est))))))
(byday (list mo we fr)))
or something like that. Of course, we can provide axioms that relate
all these symbols to an underlying world of time intervals. I'll try
to work something up in my copious spare time.
Pat's general comment:
.... As a 'standard' ontology, this sometimes
seems to me to fall between two stools. On the one hand it goes to
considerable lengths to support a variety of rather arcane and
academic alternatives, eg the two-treatments of infinity and the
nonlinear time options; but considered as a general theory it often
cuts corners and seems if anything too simple in places. On the other
hand, considered as a pragmatically useful ontology it doesn't pay
enough attention to existing standards and is probably way too
complicated for most purposes, particularly where it gets into axioms
with three or four nested quantifiers. I suspect that most users
would be happier with a quick-and-dirty version which just took a
position on infinity and linearity and density, one way or the other,
was aligned with things like ISO and XSD, and allowed people to get
simple calendering up and running quickly; and had in the background,
as it were, a more 'advanced' version which allowed one to handle
leap seconds and make all kinds of subtle distinctions without
getting confused. But then the latter had better REALLY be
general-purpose, so that it wouldn't break when considering BC dates,
or tree-rings, or relativistic corrections for GPS transmissions, or
Ramadan.
I agree, although I don't think we have to deal with tree rings,
relativity, or alternative calendars. (The ontology should not
prevent others from developing alternative calendars, however.)
More specific Hayes comments:
>4. There is a treatment of temporal aggregates. Comments solicited.
On the other hand, this seems too complicated. Maybe Im not seeing
the reasons for the complexity, but using set theory seems like
overkill right at the start. BTW, the 'clocks and calendars' section
4 of my old time-survey memo has a treatment of some of these issues.
Where might that old memo be?
BTW, a general point: some of the complexity of parts of this can be
eliminated by using CL rather than a conventional FO syntax.
Or by using a typed lambda-calculus.
I am not happy with the account here of the relationship between
durations and calendars. On the one hand, it repeats a common mistake
in treating months as duration measures (Its being a 'standard'
doesn't make it right, and repeating an error doesn't make it
better.) and in not properly handling leap seconds and other
awkward-but-real stuff; on the other hand, it seems overly
complicated.
I agree: MONTHS ARE NOT DURATIONS! RFC 2445 allows other units as
durations, but not months.
>1. Temporal arithmetic.
That ought to just be arithmetic, if durations were done properly.
Jerry actually said "duration arithmetic." One thing I miss in
DAML-Time as it stands is dimensioned quantities, like a term denoting
"3 minutes."
>The basic ontology is silent about whether time is linearly ordered.
>Thus it supports theories of time, such as the branching futures
>theory, which conflate time and possibility or knowledge.
Bad play, IMO. Confuses temporal with other issues, and repeats an old error
I don't know if it's a bad play, but we certainly are in a muddle
about what branching time _means_. As I've said before, this comes
down to what an instant is. If an instant is essentially a date, then
there's no conceivable reason to allow branching time. One might have
to maintain multiple data structures to keep track of various possible
relationships among instants, but, as Pat and I have said before,
the underlying timeline would still be totally ordered, because dates
are totally ordered. If instants differ from dates, what are they? I
maintain that they have to be situations, but I sense that others
disagree.
If you want to deny the existence of instants, then rephrase the
paragraph above in terms of intervals and ordered pairs of dates.
Here's another way to put the point: If (holds e t1) and (not (holds e
t2)), and t1 and t2 have the same date (or the same date interval),
then t1 and t2 must each denote a _something_ that associates dates
with eventualities. The burden is on anyone who denies that these
somethings are not in essence situations.
>In the basic ontology we have tried to remain neutral with respect to
>controversial issues, while producing a consistent and useable
>axiomatization. In specific applications one may want to have
>stronger properties and thus take a stand on some of these issues. In
>this section, we describe some options, with the axioms that would
>implement them. These axioms and any subsequent theorems depending on
>them are prefaced with a 0-argument proposition that says the option
>is being exercised.
Neat trick.
Yes, but the names should be clearer. Instead of total-order, use
totally-ordered-time, and so forth.
Also, to repeat and amplify previous remarks I've made:
I don't see any reason to entertain the idea that time intervals might
not be convex.
"Extensional collapse" is too alarmingly named. Plus, the name
connotes the wrong thing. "Collapse" fails if time branches into the
past as well as the future. Then two distinct intervals could have
the same endpoints. What does this have to do with the "extension" of
anything?
>The predicate during relates an eventuality to an interval, and is
>intended to say that the eventuality holds, obtains, or is taking
>place during that interval.
Well, that is ambiguous, as Im sure you know. Ie does it mean holding
throughout, continuously, or only somewhere inside?
>
><axiom id=3D"2.5-2">
> during(e,T) --> interval(T)
></axiom>
>
>If an eventuality obtains during an interval, it obtains at every
>instant inside the interval.
Ah, OK. So then if I take a trip lasting five days, am I travelling
while Im sleeping? (Or if it takes me a couple of years to write a
book, am I writing while Im having a shower? Etc.)
You maybe ought to at least *say* something about this issue.
There ought to be at least two sorts of eventualities: those that hold
at an interval if and only if they hold at every instant in the
interval, and the other kind.
>Often the eventualities in the event ontology are best thought of as
>propositions,
What other kinds of eventualities are there? (Why does one need this
2-stage approach? Seems needlessly complicated.) Whatever they are,
by the way, they can be subsumed under the proposition "so-and-so
exists" for temporal purposes. That is, temporal entities can be
considered to be exemplifications of existential propositions.
I don't understand.
>The time ontology provides ways of reasoning about the t's; their use
>as arguments of predicates from another domain would be a feature of
>the ontology of the other domain.
Right. Good move.
Incidentally, this seems to me to be a useful heuristic: the temporal
theory ought to be preserved under all variations on these other
theories, eg whether you include times as arguments or relativize
truth to them or use them as modal possible-world indices, it ought
to come out the same.
I agree.
>The relation between days and months (and, to a lesser extent, years)
>will be specified as part of the ontology of clock and calendar below.
>On their own, however, month and year are legitimate temporal units.
Hmmm. Seems to me that we need to distinguish units of duration on
the one hand, and calendering devices on the other. What 'three
months' means is something like 'starting now, go on until the same
calendar date three months in the future'. But that is NOT an
interval of time: its a class of intervals with *varying* durations.
Yes!
I don't understand the motivation for wanting months as durations.
The only one I can come up with is that in ordinary speech we often
say things like "the baby's due in three months." But ordinary speech
is an unreliable source of ontology problems, much less solutions to
them. (My old polemic on "Natural Stupidity" makes this point.) Even
in the real world, when people (or lawyers or insurance companies)
want to be precise, they say "90 days," not "three months."
>This treatment of concatenation will work for scalar phenomena in
>general. This treatment of Hath will work for measurable quantities
>in general.
True, but it is way overly complicated for most of them. Most scalar
measuring schemes have been designed to be multiplicative, so that
you don't need to get into which particular collection of inches you
are concatenating, you can just say one foot =3D 12 inches, and then
multiply. Months break this because, basically, months are determined
by the moon and all the other units are determined by the sun, and
the sun and the moon have got pretty much nothing to do with one
another.
Historically months were lunar, but now they're just arbitrary.
I really think that the only effective way to handle months is in
terms of a repeating pattern of units (the 30/31/29) pattern for the
months in a year) and being explicit about this. The same machinery
also enables you to handle leap years, leap seconds and calendar
corrections.
Except there's no pattern to leap seconds, as far as I know.
>We leave leap seconds to specialized ontologies.
Not good enough: a workable uniform treatment of time NEEDS to
consider leap seconds, if ignored they do things like breaking GPS
systems.
All you need to say is that some calendar years are not a year long,
but a year plus a second long. And all you need in order to say that
is to maintain a clear conceptual distinction between durations
(which really are on a scale) and calendaric entities (which are
really not). A year-duration is a different thing from a calendar
year.
I agree. I don't think the current DAML-Time notion of calendar day,
week, etc. is quite correct. The relevant symbols are 'da', 'daFn',
and the like. We have axioms such as
;; Axiom "4.3-2"
(iff (wk y n x)
(= (wkFn n x) y))
'x' is any proper interval, but if we want to capture the idea of a
calendar week, 'x' has to be a proper calendaric entity itself (a
month or year). I _think_ that in most places the ontology does
indeed force the third argument of 'wk' and second argument of 'wkFn'
to be appropriate intervals, but the term (wkFn n x) denotes something
even when 'x' is not calendaric, and that something makes (wk
something n x) true. Bug opportunities abound.
Of course, on top of that we have to deal with the fact that RFC 2445
and other standards say the first week of a year is the first week a
majority of whose days fall in that year.
"Granularities"
I tend to agree with Pat's comments. I also don't see why granularity
is important at this stage.
One futher stylistic comment, nothing to do with Pat's remarks:
Jerry says at one point
The days of the week have special names in English.
and similarly for months.
Every time I read this sentence I cringe a bit. The names aren't
special, _every_ language has names for days and months, and
predicates aren't names.
I think it should say something like:
We introduce predicates whose names are the same as the standard
English names for the days of the week.
-- Drew
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