|
At 3:03 PM -0500 1/23/08, Patrick Cassidy wrote:
PatH,
Many thanks for the detailed comments.
In answer to several 'why's - just because I want to
include everything
that anyone might find useful as long as it is not logically
inconsistent
with other parts.
Hmm, but that would surely lead to extremely 'inclusive'
ontologies. There is no end to the things that people might, indeed
actually would, find useful: intermittent intervals, 'fuzzy'
intervals, tolerances, a notion of acuity, the ability to specify an
interval by a propositional condition, the ability to deal with
circular time (for seasonal events and recurrent intervals), the
ability to deal with multiple granularities, the ability to consider
branching futures but also to eliminate them when they become awkward,
etc.. All these have at one time or another been seriously proposed as
vital parts of a realistic time ontology. In contrast, I have
never seen a convincing use case for putting the real line into time
reasoning. The distinction between open and closed intervals is quite
UNintuitive: it is an artifact of a certain mathematical approach to
the description of continuity, and wasn't widely accepted even among
mathematicians until the early 20th century. It still gives
high-school students trouble, and hardly anyone without a math degree
will get it exactly right.
I want an ontology that will be
useful to as many people
as possible, and my expectation is that the best way to do that is to
not
exclude anything that someone might want,
if it can be accommodated.
Might possibly want, or actually has wanted? I don't think that
the former is meaningful as a design criterion.
This
increases the complexity of the program that has to handle each
element that
has an alternative representation, but finding the proper way to
accommodate
alternatives should only have to be done once
Assuming that we have thought of them all in the first place,
which is so unlikely that it can safely be ignored :-)
, and I think it will be worth
the effort - merely a gut feeling, but a strong one.
As an example of my preferred methodology:
[PC] > > (3) two time intervals closed at the adjoining
ends both overlap
and
> meet (I think this is not permitted in Allen's algebra)
>
[PH] > Right, it is not. This would wreck all the
> algebraic time-interval reasoners. Why do you
> want to do this?
>
I would rather modify the reasoners
I should perhaps have said all the algebraic time *ontologies*.
Its not primarily a point about the efficiency of reasoning. (But in
any case, that is easy to say, but not nearly so easy to do when the
underlying algebra has 4 times as many generators, as it will have in
your case.)
to accommodate a more inclusive
ontology
But its not more inclusive, just different. The vector continuum
theory has points and intervals, treats the point b as identical to
the interval <b b>, and still preserves (a version of) the Allen
algebra. It also has a number of things that your model lacks, most
notably backward-pointing intervals with negative duration, and many
useful axiomatic simplifications (for example, *any* two points
determine a unique interval, without qualification, and meeting
intervals always uniquely determine their unique meeting-point) and
yet it doesn't need the artificial and useless distinction between
open and closed intervals.
than restrict the ontology to accommodate
existing reasoners. That's also
why I prefer FOL+ for ontologies even though DL reasoners are more
efficient.
I agree with you there, but that's not analogous. We aren't
comparing expressiveness of logics here, but rather appropriateness of
ontologies. There is a real danger of 'concept-bloat' when writing
ontologies, and it has serious consequences, as it multiplies
throughout the entire ontology. For example, if the time ontology
requires a distinction between 4 kinds of interval with the same
endpoints, and so 4 ways of meeting and so on, then every
temporal reference has to be aware of, and sensitive to, these 4-way
distinctions. There will be at least 4 kinds of event, of process,
etc.: or else there will have to be ad-hoc and pointless 'conventions'
that must be followed and remembered (continuous verbs of motion
indicate actions on closed time-intervals, etc.) And none of this is
necessary!
This is an answer in general terms,
without a specific "need"
cited, but it conform to the goal (which I think is valid) of not
restricting the foundation ontology for any reason other than
logical
inconsistency.
I don't want it *restricted*, but to use a different
mathematical basis for the time-line, in order to make it better
correspond to intuition, isn't restricting it, its just doing it
professionally.
Perhaps there will be cases where I
will conclude otherwise,
and if it turns out that this specific
"desideratum" creates a lot more
difficulty than I anticipate I would apply a more stringent
"need" criterion
to eliminate it. For now, it seems relatively
harmless
I very much doubt it. (The conflation of meeting with overlapping
isn't properly thought through yet, and is likely to be very harmful.)
But what are your arguments FOR it? Its one among many candidates, and
I don't see that it has a lot to recommend it, frankly. And in any
case, you havn't actually given us an ontology. What do the axioms
look like?
, as I anticipate
that the interval algebra can be easily modified to accommodate it,
even if
the result is less elegant than the existing theory.
Concerning two other specific points:
[PH]
> You need to be careful. Consider the tossed ball.
> There are two open meeting intervals where its vertical velocity
is
non-zero. But at the point where they
> meet it is zero. You don't want the truth of the
proposition
> (vertical velocity =/= 0) to 'leak' into that point when
they are
concatenated.
>
> BTW, this is a real issue. Points like this are central to
qualitative
physics
> reasoners and planners, which have many real applications in
industry now.
If I were to generate the event described by concatenating the before
and
after intervals, that would require an ad hoc solution, but I can't
think of
any reason why I would actually represent that event as anything other
than
the full up and down trajectory, where the zero velocity is true only
at the
one point, within an event defined by a differential
equation.
Read some of the literature on qualitative (not naive) physics.
It is all about boundary points where velocities and accelerations
change values from positive to negative. One can give entire
qualitative theories in terms of vectors of such qualitative states,
and use them in controllers, etc..
If for some
reason I did need to deal with the issue of truth at a point generated
by a
concatenation of open intervals, I would set the fluent values at
the
meeting point as intermediate between the values at those
intervals
infinitesimally before and
infinitesimally after the meeting point
Have you even tried to axiomatize any of this?? What do you mean
by "setting" a value? Or by "infinitesimal"? In
the modern mathematical framework in which the open/closed distinction
makes sense, there isn't such a thing as an infinitesimal: they don't
exist.
, both of
which fluent values should be experimentally indistinguishable, by
projection or interpolation from their values in their respective
intervals.
For the situation where one wants to represent a value as changing
abruptly
at a time point, that should only be allowed for intervals that are
open
before and closed after the point.
Hmm, I really don't like that "allowed". Allowed by
who?
Why open before and closed after? What about closed before and
open after? This looks like one of those ad-hoc conventions that one
finds the need for in order to stay sane.
For physical units including
time, I do think that some notion of
precision (granularity, tolerance) has to be included in the
reasoning
Well, QP manages to get a lot done without it. In fact, I don't
know of any practical ontology that does any reasoning about
granularity (though Jerry Hobbs might).
, but
in specific cases the tolerance can be set to zero (as in the case
of
representing differential equations).
. . . and:
[PC] > > (6) Two intervals open at the adjacent ends also
meet if those
ends
>> are defined by a common point
>
[PH]> Now you have the problem that a pair of points
> does not uniquely determine the interval between
> them, which runs counter to all
intuition and
> will destroy many calendar and interval-reasoning
> systems.
>
Since all instances of intervals will have their type defined (cc, co,
oc,
oo), each will be uniquely defined by its open and close
points.
Four kinds of interval... Four kinds of meeting... Four different
interval algebras, whose union is an algebra probably roughly 4x4 =16
times as big. The Allen transitivity table has 13x13= 169 entries:
this one will have about 2000 entries. And as far as I can see, all
this in order to gain nothing of any actual use.
PatH
PatC
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
> -----Original Message-----
> From: Pat Hayes [mailto:phayes@xxxxxxx]
> Sent: Wednesday, January 23, 2008 2:06 PM
> To: [ontolog-forum]
> Cc: Patrick Cassidy
> Subject: Re: [ontolog-forum] Time representation
>
> At 1:10 PM -0500 1/23/08, Patrick Cassidy wrote:
> >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
>
> You can't get isomorphism in a FO axiomatization.
> Why do you want continuity? Seems like density is
> enough for interval/point reasoning, and for
> calculus you need more than continuity anyway.
>
> >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)
>
> Right. This would be the way to do it. But do you
> really want all these distinctions? It means that
> any attribution of truth to an interval is forced
> to make decisions about truth at the endpoints,
> and often - Id say almost always - there is no
> way to decide such questions, no actual fact of
> the matter. Certainly there is no perceptual or
> engineering/measurement way to distinguish an
> open from a closed interval.
>
> > (2) a time point as a subtype of a closed time
interval, and
> identical to a
> >closed interval of zero length.
>
> Is there any utility in saying a point is a kind
> of interval? And what do you say about open
> intervals 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
>
> Right, it is not. This would wreck all the
> algebraic time-interval reasoners. Why do you
> want to do this?
>
> >);
> > Intervals that both overlap
and meet must both be closed at the
> meeting
> >ends and have a single time point as the overlap
interval.
>
> Makes sense. But do you want to allow any other
> things to be both points and intervals?
>
> > (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.
>
> This seems baroquely complicated (how many
> dividing operations must one keep track of??) and
> also arbitrary: why does the dividing point get
> absorbed by the later rather than the earlier
> interval?
>
> When you say equal parts: does the closed
> interval [a b] have the same duration as the open
> interval ( a b) ? Yes, surely. So why aren't
> these intervals 'equal' in the required sense (ie
> when judging duration.)
>
> > (5) catenating two intervals both open at the joining
end creates
> the point
> >of juncture.
>
> ? creates? What does that mean?
>
> You need to be careful. Consider the tossed ball.
> There are two open meeting intervals where its
> vertical velocity is non-zero. But
at the point
> where they meet it is zero. You don't want the
> truth of the proposition (vertical velocity =/=
> 0) to 'leak' into that point when they are
> concatenated.
>
> BTW, this is a real issue. Points like this are
> central to qualitative physics reasoners and
> planners, which have many real
applications in
> industry now.
>
> > (6) Two intervals open at the adjacent ends also meet
if those ends
> are
> >defined by a common point
>
> Now you have the problem that a pair of points
> does not uniquely determine the interval between
> them, which runs counter to all intuition and
> will destroy many calendar and interval-reasoning
> systems.
>
> > (7) time points are both 'part of' and 'contained in'
time
> intervals.
>
> OK
>
> > (8) the default time interval type (if defaults are
needed
>
> I have no idea what it would mean, so lets ignore this.
>
> >) 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
>
> I think its realistic for them too. A light comes
> on: even if the process of coming on takes some
> small interval of time, that interval must have a
> first point.
>
> >, 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?
>
> Probably not in the catalog in that exact form,
> no. I only considered actual axiomatic theories.
> Its impossible to specify the real line in FOL,
> for example: you need the notion of continuity,
> which is inherently second-order. But this might
> be one possible model of some of the theories, I
> havn't checked. The vector continuum treats <b b>
> as being both a point and an interval, but it
> modifies the notion of 'meet' to preserve an
> Allen-style algebra: you have to say that these
> point-intervals meet themselves. In that theory,
> <a b> does not overlap <b,b>: it meets it.
>
> > If not, is it somehow internally logically
> >inconsistent?
>
> Im sure its not inconsistent, but I am quite
> unconvinced that it would be particularly useful
> (and certainly not universally acceptable.)
>
> PaT
>
> >
> > 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.
> >> >>
> >> >>
> >> >>
>
_________________________________________________________________
> >> >> Message Archives:
http://ontolog.cim3.net/forum/ontolog-forum/
> >> >> Subscribe/Config:
> http://ontolog.cim3.net/mailman/listinfo/ontolog-
> >> >> forum/
> >> >> Unsubscribe:
mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> >> >> Shared
Files: http://ontolog.cim3.net/file/
> >> >> Community Wiki:
http://ontolog.cim3.net/wiki/
> >> >> To Post:
mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> >> >>
> >> >
> >> >
> >>
>_________________________________________________________________
> > > >Message Archives:
http://ontolog.cim3.net/forum/ontolog-forum/
> >>
>Subscribe/Config:
> http://ontolog.cim3.net/mailman/listinfo/ontolog-
> >> forum/
> >> >Unsubscribe:
mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> >> >Shared Files:
http://ontolog.cim3.net/file/
> >> >Community Wiki:
http://ontolog.cim3.net/wiki/
> >> >To Post:
mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> >> >
> >>
> >>
> >> --
> >>
-------------------------------------------------------------------
> --
> >> IHMC
(850)434 8903 or (650)494 3973 home
> >> 40 South Alcaniz St. (850)202
4416 office
> >> Pensacola
(850)202 4440 fax
> >> FL 32502
(850)291 0667 cell
> >>
phayesAT-SIGNihmc.us
http://www.ihmc.us/users/phayes
> >>
> >>
> >>
_________________________________________________________________
> >> Message Archives:
http://ontolog.cim3.net/forum/ontolog-forum/
> >> Subscribe/Config:
http://ontolog.cim3.net/mailman/listinfo/ontolog-
> >> forum/
> >> Unsubscribe:
mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> >> Shared Files: http://ontolog.cim3.net/file/
> >> Community Wiki: http://ontolog.cim3.net/wiki/
> >> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> >>
> >
> >
>
>_________________________________________________________________
> >Message Archives:
http://ontolog.cim3.net/forum/ontolog-forum/
> >Subscribe/Config:
http://ontolog.cim3.net/mailman/listinfo/ontolog-
> forum/
> >Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> >Shared Files: http://ontolog.cim3.net/file/
> >Community Wiki: http://ontolog.cim3.net/wiki/
> >To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> >
>
>
> --
>
---------------------------------------------------------------------
> IHMC
(850)434 8903 or (650)494 3973 home
> 40 South Alcaniz St.
(850)202 4416 office
> Pensacola
(850)202 4440 fax
> FL 32502
(850)291 0667 cell
> phayesAT-SIGNihmc.us
http://www.ihmc.us/users/phayes
--
---------------------------------------------------------------------
IHMC
(850)434 8903 or (650)494 3973 home
40 South Alcaniz St.
(850)202 4416 office
Pensacola
(850)202 4440 fax
FL 32502
(850)291 0667 cell
phayesAT-SIGNihmc.us
http://www.ihmc.us/users/phayes
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01)
|