# Response to Pat Hayes' comments on time ontology

From: Jerry Hobbs (hobbs@ai.sri.com)
Date: 04/30/02

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```Some responses to Pat's comments:

> >
> >>  > It will be useful in characterizing clock and calendar terms to have
> a
> >>  > relation between instants and intervals that says that the instant is
> >>  > inside or the start of the interval.
> >>  >
> >>  >         in-interval(t,T) <--> [start-of(T) = t v inside(t,T)]
> >
> >>  This is the relation of 'temporalPart' in the SUMO.
> >
> >Actually, this relation does not include the ends of intervals, only
> >the starts.  The reason for this is my intuition that clock and
> >calendar intervals are half open, including the start but not the end.
> >I.e. midnight is part of the next day.
>
> I think that thinking of them as either open or closed might be a bad
> idea. And I can see no rational reason for the asymmetry here. Why is
> midnight part of the *next* day, again?? I tend to talk about
> midnight *tonight*, so that midnight betweenTuesday and Wednesday is
> part of Tuesday. Maybe that's because I regularly stay awake past
> midnight, of course.

I think of 3 a.m. as part of the previous day.  For me, the new day
begins when I wake up in the morning.  But I don't think this should
be the basis of an ontolgy.

It seems to me that it's cleaner to have all times of the form 12:xx
be part of the same hour and day, even when xx is 00.  Similarly all
times of the form 10:xx should be part of the same hour, all times of
the form 10:15:xx should be part of the same minute, etc.

.....................

> >>  > 2.4.  Linking Time and Events:
> >>  >
> >>  > The time ontology links to other things in the world through four
> >>  > predicates -- at-time, during, holds, and time-span-of.  We assume
> >>  > that another ontology provides for the description of events -- either
> >>  > a general ontology of event structure abstractly conceived, or
> >>  > specific, domain-dependent ontologies for specific domains.
> >>  >
> >>  > The term "eventuality" will be used to cover events, states,
> >>  > processes, propositions, states of affairs, and anything else that can
> >>  > be located with respect to time.  The possible natures of
> >>  > eventualities would be spelled out in the event ontologies.
> >
> >>  We don't have anything like the notion of "eventuality"
> >>  in the SUMO, and this for good reason, I think.  The sense in
> >>  which a proposition is true at a particular time is very
> >>  different from the sense in which a process or event occurs
> >  > at a particular time.
>
> I agree that eventualities are a crock, but Im not sure about that
> last claim. I think that these two senses can in fact be subsumed
> into a common picture.
>
> >I'm not arguing for eventualities here, but only using it for a cover
> >term for anything that can be located in time.
>
> What I would call a 'temporal thing'. Would you include solid
> physical things in that category, eg people, sofas, things like that?
>
> >Distinctions between
> >propositions, events, processes, states, and so on are a matter for
> >the ontology of events, etc., and not for the time ontology.
> >
> >However, I should not have used "eventuality" as a predicate in the
> >axioms below constraining the arguments of at-time and during, which
> >should have been merely
> >
> >       at-time(e,t) --> instant(t)
> >       during(e,T) --> interval(T)
> >
> >What e is is a matter for the event ontology to specify.

Pat, you can do a global replace of "temporal thing" for "eventuality"
in all my messages.  It is just a word I am using for things that can
be located with respect to time.  It has no status in the formal
development.

I would expect there to be much less agreement on an ontology of
events than on an ontology of time.  I can imagine four or five
possible largely incompatible treatments of events that different
users might find useful in different contexts.  That is why I wanted
to maintain a clean separation between events and time.

I can imagine some ontology developers having to treat people and
sofas as time-dependent for their application, and others treating
them as time-independent.  That's not for the ontology of time to
specify.

...........................

> >>  > The predicate at-time relates an eventuality to an instant, and is
> >>  > intended to say that the eventuality holds, obtains, or is taking
> >>  > place at that time.
> >>  >
> >>  >          at-time(e,t) --> eventuality(e) & instant(t)
> >>  >
> >>  > 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.
> >>  >
> >>  >          during(e,T) --> eventuality(e) & interval(T)
> >>  >
> >>  > If an eventuality obtains during an interval, it obtains at every
> >>  > instant inside the interval.
> >>  >
> >>  >          during(e,T) & inside(t,T) --> at-time(e,t)
> >
> >>  We use 'holdsDuring' and 'time' for these relations in the SUMO.
>
> I like the SUMO names better here. Why is there any need to
> distinguish these cases, since there is no sharp distinction between
> intervals and timepoints? I think that making them the same might
> make granularity changes easier, since an interval at one scale looks
> like a point at another.
>
> >
> >................
> >
> >>  > Often the eventualities in the event ontology are best thought of as
> >>  > propositions, and the relation between these and times is most
> >>  > naturally called "holds".
>
> That might be unfortunate, since 'holds' is also widely used to
> encode higher-order assertions into first-order, as in holds(P, x, y)
>
> I am in general rather nervous about things like 'holds', which
> smells awfully like a kind of truth-predicate. Why not just assert
> the thing that is supposed to 'hold'? If it can be true or false, it
> should be assertable in the language. All of Jerry's 'eventualities'
> way of talking is just an elaborate way of avoiding quantification
> over higher-order entities, but we can do that for free in KIF, so
> just go ahead and do it. (If you want to use classical FOL notation,
> do a uniform under-the-hood translation using 'holds', but there's
> really no need to do that.)
>
> >  holds can be defined in terms of at-time
> >>  >>and during:
> >>  >
> >>  >          holds(e,t) & instant(t) <--> at-time(e,t)
> >>  >          holds(e,T) & interval(T) <--> during(e,T)
> >
> >This relation of "holds" maps to 'holdsDuring' in the SUMO.

Because we should be able to interface the time ontology with a
variety of event ontologies, I tried to provide various predicates
relating the two.  Different communities are typically comfortable
with different such predicates or operators.  I would be perfectly
happy if we could agree on a single predicate that would work for
propositions, events, states, and time-dependent objects, and for
instants and intervals both.

..........................

> >>  > The predicate time-span-of relates eventualities to instants or
> >>  > intervals.  For contiguous states and processes, it tells the entire
> >>  > instant or interval for which the state or process obtains or takes
> >>  > place.
> >>  >
> >>  >          time-span-of(T,e) --> temporal-entity(T)
> >>  >          time-span-of(T,e) & interval(T) --> during(e,T)
> >>  >          time-span-of(t,e) & instant(t) --> at-time(e,t)
> >>  >          time-span-of(T,e) & interval(T) & ~inside(t1,T)
> >>  >                  & ~start-of(t1,T) & ~end-of(t1,T)
> >>  >              --> ~at-time(e,t1)
> >>  >          time-span-of(t,e) & instant(t) & t1 =/= t --> ~at-time(e,t1)
> >>  > >
> >>  > time-span-of is a predicate rather than a function because until the
> >>  > time ontology is extended to aggregates of temporal entities, the
> >  > > function would not be defined for noncontiguous eventualities.
>
> We could just say it is the convex hull, ie the smallest enclosing
> contiguous interval. As in 'I spent 1971 writing my thesis'.

You also spent 1971 sleeping, in that sense.

There are two distinct notions here: the exact collection of time
intervals an event was taking place, and the convex hull of that
collection.  I'm sure both are useful.  In our future development of
an ontology of temporal aggregates, the predicate _convex-hull_ is
something we will want to define.

.........................

> >>  > Different communities have different ways of representing the times
> >>  > and durations of states and events (processes).  In one approach,
> >>  > states and events can both have durations, and at least events can be
> >>  > instantaneous.  In another approach, events can only be instantaneous
> >>  > and only states can have durations.  In the latter approach, events
> >>  > that one might consider as having duration (e.g., heating water) are
> >>  > modeled as a state of the system that is initiated and terminated by
> >>  > instantaneous events.  That is, there is the instantaneous event of
> >>  > the start of the heating at the start of an interval, that transitions
> >>  > the system into a state in which the water is heating.  The state
> >>  > continues until another instantaneous event occurs---the stopping of
> >>  > the heating at the end of the interval.  These two perspectives on
> >>  > events are straightforwardly interdefinable in terms of the ontology
> >>  > we have provided.  This is a matter for the event ontology to specify.
> >  > > This time ontology is neutral with respect to the choice.
> >
> >>  The inherent complexity of these distinctions is one reason why we don't
> >>  distinguish states from events under 'Processes' in the SUMO.
> >
> >A DAML time ontology stands to gain the most users if it supports a
> >wide spectrum of community practices.
>
> Even better, if it both supports them all and also provides ways to
> reconcile or map between them.

Agreed.  In this particular case the mapping is straightforward.

.........................

> >>  > Finally, we would like to say that the set S covers x.  A simple way
> >>  > to say this is as follows:
> >>  >
> >>  >          Hath(S,N,u,x)
> >>  >              --> (A t)[inside(t,x)
> >>  >                           --> (E y)[member(y,S) & in-interval(t,y)]]
> >
> >>  We use 'duration' to express the relationship between a
> >>  'TimePosition' and a 'TimeDuration' in the SUMO.
> >
> >The problem is to say that any point in an interval in a point in one
> >of the subintervals of which it is comprised.
>
> That might be dangerous. For example, suppose I contains J meeting K
> (all intervals). For some purposes, you might want to say that the
> meeting-point is in I but not in J or K, and there might not be any
> other subintervals. In general I would suggest avoiding this kind of
> density assumption unless it is really needed. What do you need this
> axiom for?

The problem is to say that the set of smaller unit intervals _covers_
the larger interval.  Your objection is not valid because the
predicate "in-interval" was defined as inside or starting.

..........................

> >>  > To accomodate this, the above axiom can be loosened by applying it
> >>  > only when the instant t is located in _some interval_ of size u.  The
> >>  > axiom above would be modified as follows:
> >>  >
> >>  >          Hath(S,N,u,x)
>
> Hath?? With four arguments?? Nobody is going to use this, Jerry.

In fact, I think it is cleaner to separate out two notions here, and
it will also help in talking about durations of temporal aggregates:

concatenation(x,S):  a set S of smaller temporal entities
concatenates
into a larger temporal entity x.
Hath(N,u,x):  the smaller temporal entities which concatenate to x
are all intervals whose duration is a particular unit u, and
there are N of them.

I will rewrite this section along those lines in the next day or two.

.......................

> >>  > Time zones should not be thought of as geographical regions.
>
> I disagree: I think they are exactly geographical regions. Maybe of a
> particular kind, but certainly geographical. They are contiguous
> regions of space on the surface of the earth. You can drive in and
> out of them, crossing their boundaries.
>
> >  Most
> >>  > places change their time zone twice a year
>
> I presume you mean summer time? Calling that a change of time ZONE
> seems wrong to me.
>
> Might it not be simpler to just refer all times to GMT?

That's the Chinese Communist solution.  All of China is on Beijing
time.  In order to get around this, the people of Xinjiang province,
in far west China, talk about Beijing time and Xinjiang time, and
always have to tack on the time zone they're using.  In Kashgar in far
west Xinjiang, they have three designations they use -- Beijing,
Xinjiang, and Kashgar time.

Joe's Pizza may not want to list its business hours in GMT.

> >, and a state or county
> >>  > might decide to change its time zone, e.g., from Central Standard to
> >>  > Eastern Standard.
>
> OK, and it can also change its county or state affiliation. This
> doesn't seem like an argument against time-zones being geographical.
>
> >Rather it is better to have a separate ontology
> >>  > articulate the relation between geographical regions X times and time
> >>  > zones.  For example, it would state that on a certain day and time a
> >>  > particular region changes its time zone from Eastern Standard to
> >>  > Eastern Daylight.
> >
> >>  I agree that making time zone a subclass of geographical
> >>  region is a less than optimal solution to the problem (the
> >>  solution adopted in the SUMO, by the way), but I don't
> >>  think that I understand the counterproposal.
> >
> >Think of a time zone as its own kind of legal entity.
>
> Many geographical regions are legal entities already, so I don't see
> the need for the distinction here.

I think the confusion here is caused by my use of the word "zone".
*PST* is not a zone, or a geographical region.  It is a way of
computing the time, relative to a world-wide system of computing time.
Let's just call it a "time standard".  For each time standard, there
is a zone, or geographical region, and a time of the year in which it
is used for describing local times.  Where and when a time standard is
used have to be axiomatized, and this involves interrelating a time
ontology and a geographical ontology.

Conflating time zones (i.e., geographical regions) and time standards
is likely to cause problems in several situations.  For example, the
Eastern Standard zone and the Eastern Daylight zone are not identical,
since most of Indiana is on Eastern Standard time all year.  I
understand that the state of Arizona and the Navajo Indian
Reservation, two overlapping geopolitical regions, have different time
standards -- one is Pacific and one is Mountain.  (I don't know the
facts here.)

..........................

> >>  >                             5.  Deictic Time
> >>  >
> >>  > Deictic temporal concepts, such as ``now'', ``today'', ``tomorrow
> >>  > night'', and ``last year'', are more common in natural language texts
> >>  > than they will be in descriptions of Web resources, and for that
> >>  > reason we are postponing a development of this domain until the first
> >>  > three are in place.  But since most of the content on the Web is in
> >>  > natural language, ultimately it will be necessary for this ontology
> to
> >>  > be developed.  It should, as well, mesh well with the annotation
> >>  > standards used in automatic tagging of text.
> >>  >
> >>  > We expect that the key concept in this area will be a relation
> >>  > _now_ between an instant
>
> Why instant? It might be more useful to allow an interval _now_. Then
> the communication constraint is that our 'nows' overlap, and the
> presumption is that we are communicating in the intersection: but
> neither of us really needs to know that, for most purposes.

I agree that "now" should be viewed as an interval, or at least as a
temporal entity.

.......................

> >I am more confident than you that problems with "now" can be worked
> >out, and I think the notion of a time of composition or validity of a
> >web page is
>
> Whoa, those are DIFFERENT notions, surely. What temporal DB folk call
> transaction and valid time respectively.
>
> >an essential notion to have in DAML

I agree they are different, and insofar as we develop an ontology of
deictic time, we should keep these distinct.

-- Jerry
```

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