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At 4:33 PM -0500 1/23/08, Patrick Cassidy wrote:
Yes, if possible, at least some critical
mass of ontologists should adopt
some model and notation for time representation that can serve as a
standard
for those who do not have some inconsistent alternative that they
feel
strongly about. I would expect that most potential users don't
care about
the details of an ontology standard as long as it serves to provide
some
degree of wide interoperability, and can serve their own purposes.
That is
why I think it is a good idea to include in a foundation ontology all
of the
elements that anyone wants that are not logically inconsistent with
others.
That does not define one possibility, however. Being
inconsistent with is symmetrical. If my time ontology is
inconsistent with yours, which of us gets to be in the single accepted
standard?
For individual applications, one only has
to use the parts one needs, but as
long as there are translations to other views ("bridging
axioms"),
applications using that foundation can be semantically
interoperable.
The best way to achieve interoperability is to agree on a
minimal useful ontology, which supports the concepts and
reasonings that everyone can agree on, and leaves room for a number of
(possibly inconsistent) extensions. So for example is time discrete,
dense or continuous? There simply is no possibility of agreement here,
and the alternatives cannot be made consistent with one another. So
the agreed common ontology should be carefully and painstakingly
agnostic on the matter. Similarly for questions like: Is time
infinite? Can intervals be infinite? Is there a point at
infinity? Do intervals contain their endpoints (ie are they open or
closed?) All of these have been investigated fairly thoroughly and
their relationships are understood quite well. (BTW, a fabulous
reference here, though now rather old, is van Bentham's book "The
logic of time", Reidel 1983.)
It was this notion that was the genesis of the "Time
Catalog" and the reason for its format, and I know that Jerry
Hobbs used a similar methodology when designing OWL-Time.
PatH.
Pat
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Sharma, Ravi
> Sent: Wednesday, January 23, 2008 1:47 PM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Time representation
>
> PatC
> Yes but we as community need to converge on a convention and
practice
> for CoP so that we can talk about different times, overlaps,
periods,
> scales, accuracies, when we want to represent concepts and
synchronize
> tool interoperability in future.
> Thanks.
> Ravi
>
> (Dr. Ravi Sharma) Senior Enterprise Architect
>
> Vangent, Inc. Technology Excellence Center (TEC)
>
> 8618 Westwood Center Drive, Suite 310, Vienna VA 22182
> (o) 703-827-0638, (c) 313-204-1740 www.vangent.com
>
>
>
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
Patrick
> Cassidy
> Sent: Wednesday, January 23, 2008 1:11 PM
> To: '[ontolog-forum] '
> Subject: Re: [ontolog-forum] Time representation
>
> PatH,
> Thanks for the answer.
> The implementation of Time that I would like to
use is one that I
> couldn't find in the Time Catalog - though I may not have
interpreted
> all of
> the axioms correctly. What I would like is a representation
of Time as
> isomorphic to the real line with:
> (1) open, closed and semi-open intervals, all
distinguishable and
> specified
> by their endpoints (whether or not the endpoint is included in
the
> interval)
> (2) a time point as a subtype of a closed time interval,
and identical
> to a
> closed interval of zero length.
> (3) two time intervals closed at the adjoining ends both
overlap and
> meet
> (I think this is not permitted in Allen's algebra);
> Intervals that both overlap and
meet must both be closed at the
> meeting
> ends and have a single time point as the overlap interval.
> (4) dividing a time interval at a point gives rise
(depending on the
> dividing operation) to either (a) two time intervals, each having
a
> closed
> end with the point of division (and conversely, joining two
time
> intervals
> that meet at closed ends merges the common point, which is a
single
> ordinary
> point); or (b) two intervals open at the point of division; or
(c) one
> interval (the earlier one) open and one (the later one) closed at
the
> point
> of division. Operations a and b can divide an interval into
two equal
> parts, if the starting interval ends are both closed or both
open.
> Operation c can equally divide a closed-open interval.
> (5) catenating two intervals both open at the joining end
creates the
> point
> of juncture.
> (6) Two intervals open at the adjacent ends also meet if
those ends
> are
> defined by a common point
> (7) time points are both 'part of' and 'contained in' time
intervals.
> (8) the default time interval type (if defaults are needed)
is one
> closed
> at the lower end and open at the upper end -
> (This type is used to specify AM or
PM in a day).
> (9) Events that occur at a single time point imply a
preceding
> interval
> open at that point, in which the event state differs from the
state at
> (and
> for some interval after) that point. Though unrealistic for
physical
> events, this can be used to specify socially defined events, such
as
> someone
> becoming president at a particular time point.
>
> But I didn't see (and may have missed) a single
theory that has all
> of
> those requirements in the time catalog. Is such a theory
actually in
> the
> time catalog - or elsewhere? If not, is it somehow
internally
> logically
> inconsistent?
>
> PatC
>
> Patrick Cassidy
> MICRA, Inc.
> 908-561-3416
> cell: 908-565-4053
> cassidy@xxxxxxxxx
>
> > -----Original Message-----
> > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-
> > bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> > Sent: Wednesday, January 23, 2008 12:12 AM
> > To: [ontolog-forum]
> > Subject: Re: [ontolog-forum] Time representation
> >
> > At 11:31 PM -0500 1/22/08, Patrick Cassidy wrote:
> > >Just a question about one point (so to speak):
> > >
> > >>
> > >> Re PTim: I realize that calling an interval a
point is
> > problematical.
> > >> But in anything that has to do with the
physical world, there is
> no
> > >> way to specify a true point. Perhaps a
better term would be
> "grain
> > >> in time", abbreviated
"Grit".
> > >>
> > >
> > >Has anyone observed any problems of *logical
consistency* in
> > classifying a
> > >point on a line as being identical to a closed interval
of zero
> > length, with
> > >beginning and end points identical?
> >
> > I presume you mean, interval on the real line.
> > None: this is quite consistent. This model
> > (actually several versions of it) is discussed in
> > the 'time catalog'. But it does produce some
> > complications. For example, consider a ball
> > tossed into the air. At one point in its
> > trajectory, its vertical velocity is zero. If
> > this is a closed interval [b,b], then the
> > intervals of positive and negative vertical
> > velocity must be open (or semi-open) intervals
> > (a,b) and (b,c). Now, these intervals have the
> > same endpoint, so they apparently meet (in the
> > sense used by Allen's interval algebra). Yet
> > there is an interval *between* them, so they
> > apparently cannot meet. So this model seems to be
> > incompatible with the Allen algebra, which is a
> > major problem. The ontology called the 'vector
> > continuum' there takes this idea and develops it
> > axiomatically rather than presuming the real
> > line, and gives a temporal ontology which I think
> > is quite neat. But it has some apparent oddities,
> > eg it allows negative intervals (which turn out
> > to be quite useful.) And it isn't possible
> > (AFAIK) to interpret it in the
real line.
> >
> > > Or are the 'point' and 'interval'
> > >classifications merely two different views of the same
thing?
> >
> > Really, there is no simple answer to this
> > question. Try reading some of the options
> > described in the catalog. I think the various
> > intuitions are reasonably well explained there.
> >
> > PatH
> >
> > >
> > >PatC
> > >
> > >Patrick Cassidy
> > >MICRA, Inc.
> > >908-561-3416
> > >cell: 908-565-4053
> > >cassidy@xxxxxxxxx
> > >
> > >> -----Original Message-----
> > >> From:
ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-
> > >> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John
F. Sowa
> > >> Sent: Monday, January 21, 2008 12:48 PM
> > >> To: [ontolog-forum]
> > >> Subject: Re: [ontolog-forum] Time
representation
> > >>
> > >> Pat,
> > >>
> > >> The position I most strongly advocate is not
a specific ontology,
> > >> but a framework of conventions for organizing
a multiplicity
> > >> of special cases (not necessarily consistent
with one another),
> > >> making the
implicit relationships explicit, and providing tools
> > >> and guidelines for mixing and matching.
The lattice of theories
> > >> is an example. Robert Kent's IFF is a
much more ambitious
> example.
> > >>
> > >> I would recommend a fairly simple framework
for starters, since
> > >> there's a danger of freezing half-baked ideas
before they're
> fully
> > >> baked. (RDF, for example, was hardly
out of the oven before
> > >> Tim Bray tried, unsuccessfully, to pull it
back in.)
> > >>
> > >> > Do you have any granularity
axioms? That is one of the
> hardest
> > >> > ontological problems, in my
experience.
> > >>
> > >> There are so many hard problems, it's hard to
say which are
> harder.
> > >> But the idea of taking the least significant
digit as the
> criterion
> > >> for implicit granularity is fairly common for
experimental data
> > >> (unless some explicit margin of error is
stated).
> > >>
> > >> Re PTim: I realize that calling an interval a
point is
> > problematical.
> > >> But in anything that has to do with the
physical world, there is
> no
> > >> way to specify a true point. Perhaps a
better term would be
> "grain
> > >> in time", abbreviated
"Grit".
> > >>
> > >> John
> > >>
> > >> PS re HTML email formats: Your note of
11:18 was in a readable
> > font
> > >> for Thunderbird, but your note of 11:37
appeared in a tiny, tiny
> > font.
> > >> I had to increase the font size by two steps
to make it the same
> as
> > >> the previous note. But then the fonts
for all other notes were
> too
> > >> big, and I had to decrease the default by two
steps.
> > > >
> > >> At least each of your notes was entirely in
one font size. I've
> > >> received some email in which each paragraph
was in a
> progressively
> > >> smaller font. That's why I hate HTML
email.
> > >>
> > >>
> > >>
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