Vol. 2, Nr. 3  Editor: Erik Sandewall  31.3.1998 
Today 
Forthcoming conferences and workshops  
ETAI Received Articles 
Discussion about received articles  
TopicOriented Discussions 
Causality and Ramification  
Ontologies for time  
Workshop Discussions 
Discussions about Articles at Commonsense workshop 
Today 
ETAI Received Articles 
Additional debate contributions have been received for the following article(s). Please click the title of the article to link to the interaction page, containing both new and old contributions to the discussion.
Antonis Kakas and Rob Miller
Reasoning about Actions, Narratives and Ramification
TopicOriented Discussions 
From: Eugenia Ternovskaia on 2.3.1998
Erik Sandewall wrote:
maybe the section on "related work" in research papers ought not to be our only mechanism for assembling topicspecific surveys and bibliographies, and possibly the present debate forum could serve as a complement. Additional contributions are invited to this account of recent history, therefore. 
A few notes about earlier work on the solution to the frame and ramification problems based on the notion of causation.
In connection with the frame problem, an important step forward was the idea
I think it was proposed in Lifschitz's 1987 paper [sBrown8735], but it needs a check. Vladimir, could you remind us?
Reiter, basing his solution on the previous work by Pednault, Haas and
Schubert, appeals to the same two principles
[sLifschitz91359]. He
specifies the conditions making
a fluent to hold and not to hold by FO formulas
The main lesson we can derive from this work is that no special nonlogical symbol (predicate) is necessary to capture causal information in classical logic.
With respect to the ramification problem, Elkan
[ccscsi92221] considers a ``stuffed room''
domain, a variant of the ``suitcase example''. He argues that the ambiguity
problem can be resolved using an explicit notion of causation.
He uses two predicates,
From: Pat Hayes on 14.3.1998
Im largely in agreement with Jixin about points and intervals, although I dont think its got anything to do with knowledge, and I think there's a simpler way to say it all.
First, just forget about whether intervals are open or closed.
This issue arises only if we insist (as the standard mathematical
account of the continuum does) that an interval is a set of points.
But if we take points and intervals as basic, there is no need to do
this. Points, as
Allen suggested long ago, can be thought of as places where intervals
meet each other, not as the substance out of which intervals are
constructed. It took me a long time to see how powerful this idea is.
The question of which interval 'contains' the meeting point is
meaningless. This gives a very simple, elegant formulation in which
points are totally ordered, intervals are uniquely defined by their
endpoints (which are also the points they fit between) and two
intervals meet just when the endpoint of the first is the startpoint of
the second. That's all the structure one needs. Truths hold during
intervals. One can allow instantaneous intervals, whose endpoints are
identical and which have no duration. One can, if one wishes, identify
the interval
(Instantaneous intervals have the odd property of meeting themselves, by the way; in fact this is a way to characterise them without mentioning points explicitly. It is also perfectly consistent to have 'backward' intervals whose end is earlier than their beginning, and which have negative durations. Axiomatic details can be found in a rather long document available as two postscript files
http://www.coginst.uwf.edu/~phayes/TimeCatalog1.ps http://www.coginst.uwf.edu/~phayes/TimeCatalog2.psOne can cast the whole theory in terms of a single threeplace relation MEETSAT between two intervals and a point, much as Allen's original theory can be cast in terms of MEETS.)
In this theory, to talk of the set of points 'in' an interval requires
one to specify what it means for a point to be 'in' an interval. If a
point is later than the beginning and earlier than the end, its clearly
in the interval, but we have some freedom with the endpoints. One could
insist that interval endpoints are 'in' the interval. But this is now
OK, since truths hold not at points but during intervals, so the
apparent contradiction of the light being both on and off at the
splitting point simply doesnt arise. The light isn't either on or off
at a single point: if you want to know whether the light was on or not,
you have to say which interval you are talking about. P may be true
during
Jixin says that "one cannot talk about anything about the switching
point P, which is intuitively there anyway." Well, the point is
certainly there, and we can talk about it (for example, its relation to
other points and intervals) but the question is whether it makes sense
to say that something is true at it. Some truths may be instantaneous,
ie true only at points; others make sense only when asserted to hold
during noninstantaneous intervals. Lights being on or off, for example,
might be enduring, while changes in illumination, or isolated flashes,
can be instantaneous. So for example suppose it is dark during
interval
Pat Hayes
From: Jixin Ma on 17.3.1998
After reading Pat's answers to our claims/arguments about the ontology for time, we would like to raise the following questions/arguments:
1. First of all, it is not clear what's the exact role that time points play in Pat's formulation, although, according to Erik's understanding, Pat Hayes "argues in favour of an ontology for time where intervals are the only elementary concept and timepoints play a secondary role". As Pat points out in his answers (in agreement with our opinion as stated in our claims), "if we take points and intervals as basic, there is no need to do this", i.e., deal with the question of whether intervals are open or closed. However, it is not clear what's the exact meaning of "taking points and intervals as basic". Are they both taken as primitive temporal objects, or, as Allen suggests, points are thought as places where intervals meet each other?
2. Pat argues that "the question is whether it makes sense to say that something is true at points". However, his argument is quite confused: in the first place, he claims "truths hold not at points but during intervals" (as for the case when one insists that interval endpoints are "in" the interval). Later, he states "Some truths may be instantaneous, ie true only at points; others make sense only when asserted to hold during noninstantaneous intervals". So, what's the answer to the question "whether it makes sense to say that something is true at points"?
3. Pat's claims that one may identify interval
I. As noted by Pat himself, "an instantaneous interval meets itself", though the "basic" points are totally ordered. How to characterise the relation between them? Pat's gives a suggestion: to characterise them without mentioning points explicitly. Then, what's the relationship between points and intervals?
II. How to define other relationships between intervals like those
introduced by Allen? For instance, it is intuitive to say that
III. By saying
4. Pat argues that "I'm largely in agreement with Jixin about points and intervals, although I dont think its got anything to do with knowledge". But it does. In fact, as pointed out by Pat himself, "if you want to know whether the light was on or not, you have to say which interval you are talking about". In other words, if the (additional) knowledge of "which interval you are talking about" is given (e.g., in terms of which interval is open/closed at the switching point, or in terms of the corresponding meets relations  "knowledge"?), we can say whether the light was on or not.
5. Pat also argues that his formulation is simpler (and elegant). In what aspects, compared with which formulation? It seems that it still needs a lot of axioms to characterise the formal structure, especially when issues such as density, linearity, boundness, etc, are to be addressed.
Jixin & Brian
From: Pat Hayes on 27.3.1998
Sorry, I wasnt sufficiently clear, and my carelessness in using intuitive phrasing led to misunderstanding.
First, in my view there is no single answer to many of the issues that Jixin raises. One can make various choices, each internally consistent but not consistent with the others. (That is why I called the cited paper a 'catalog' of time theories, rather than a single theory of time.) This freedom means that one must be clear which alternative one is using, as confusion follows when one tries to put together bits and pieces of incompatible views. (For example, the critique of Allen's account by Galton in [jaij42159] in 1990 (wrongly) assumes that Allen's intervals are sets of points on the real line.) Having said this, however, there does seem to be a simple, basic, account which can be extended in various ways to produce all the other alternatives, and this core theory is the one I was referring to.
Second, I dont agree with Erik's introduction of my note (14.3) as putting intervals before points. As Allen and I showed some time ago, the choice is arbitrary, since points can be transparently defined in an interval theory and vice versa, so the choice of either one as somehow more basic is, er, pointless; and one gets a more useful account simply by allowing them both as primitive. (Actually, if anything, the simple theory I outlined seems more to rely on points as basic, since an interval there is completely defined by its two endpoints and has no other structure, and all the temporal relations between intervals can be inferred from the total ordering of points.)
Jixin asks:
However, it is not clear what's the exact meaning of "taking points and intervals as basic". Are they both taken as primitive temporal objects, or, as Allen suggests, points are thought as places where intervals meet each other? 
Both. These arent incompatible alternatives. The basic idea in the 'simple' theory is essentially Allen's, that points are meetingplaces. Still, there's no harm in being able to mention these meetingplaces as real objects, and doing so makes it easier to say quite a lot of things, such as 'when' some change happens. Clock times seem to be associated more naturally with points than intervals, for example.
2. Pat argues that "the question is whether it makes sense to say that something is true at points". However, his argument is quite confused: in the first place, he claims "truths hold not at points but during intervals" (as for the case when one insists that interval endpoints are "in" the interval). Later, he states "Some truths may be instantaneous, ie true only at points; others make sense only when asserted to hold during noninstantaneous intervals". 
(In the above I was careless at the place marked by boldface, sorry. I should have said 'pointlike interval'. It gets hard to speak about this stuff clearly in English, since I need to distinguish our intuitive notion of 'point' from the way that a particular theory encodes this intuition, and different theories do it differently. I will use scarequotes to refer to the intuitive concept.)
So, what's the answer to the question "whether it makes sense to say that something is true at points"? 
There is no (single) answer: one can craft the theory to suit various
different intuitions on matters like these. The way I prefer, myself, is to
say that propositions hold only during intervals, so that it is simply
illformed to assert a proposition of a single point; but to allow the
possibility of pointlike intervals, of the form
This doesnt require us to say that every point fills an interval, notice:
since 'interval' is a basic predicate, it is perfectly consistent to say
_{ } pointlike(i) <> begin(i) = end(i) 
one can, for example, say something like
_{ } illuminated(i) v dark(i) ·> ¬ pointlike(i) 
so that the light is neither on nor off AT the switching point. In this theory, every proposition has a 'reference interval' during which it is true, and a proposition might not be true of subintervals of its reference interval. (Though some propositions might be. This kind of distinction has often been made in the linguistic literature. Note however that this intuition is basically incompatible with the idea that an interval is identical to the set of the points it contains.)
3. Pat's claims that one may identify interval 
We certainly need something corresponding to 'points', I agree. I meant only that the formal theory can be crafted in the way Ive outlined above, or alternatively by identifying the pointlike intervals with their endpoints, and allowing a proposition to hold at a single point. This is in many ways more intuitively transparent but it is formally a bit more awkward, since pointlike isnt definable any more, and one has to put in special axioms forbidding points to meet each other. The 'reference interval' of a proposition could now be a single point in the theory. This is essentially the theory that Allen and I described in our 1985 IJCAI paper [cijcai85528], though it takes a little work to see it.
Let's consider the case that we do
(in fact, for general treatments, we do need them). For this case,
Pat's states that
if 
Yes, exactly. Interval relations are comletely determined by endpoint orderings,and Allen's huge transitivity table can be painstakingly derived from the assumption of total ordering. That's all it amounts to, in fact.
Below
are some problems with this formulation:
I. As noted by Pat himself, "an instantaneous interval meets itself", though the "basic" points are totally ordered. How to characterise the relation between them? Pat's gives a suggestion: to characterise them without mentioning points explicitly. Then, what's the relationship between points and intervals? 
The relations are quite simple and transparent: intervals lie between endpoints, and points have intervals extending between them. Selfmeeting is the intervalinterval relation corresponding to equality in the point ordering. Again, if one has an intuitive objection to selfmeeting intervals, then one can take the second alternative mentioned earlier. (All these alternatives are got by extending the basic theory.)
II. How to define other relationships between intervals like those
introduced by Allen? For instance, it is intuitive to say
that 
True, and indeed the Allen relations only have their usual transitivity properties when applied to intervals which are nonpointlike and forwardoriented. Of course both these are properties expressible in the theory, so that the Allen transitivity relationships can be stated there, suitably qualified. (When the alternative extension axioms are added, the qualifications become tautologous.)
BTW, the claim that "meets" and "before" being exclusive is "intuitive" depends on how one's intuition is formed. Part of what I learned by having to construct alternative formalisations is that intuition is very malleable. Having gotten used to pointlike intervals, I dont find this exclusivity condition at all intuitive.
III. By saying 
But these cases only make sense if one thinks of interval and points in the usual mathematical way, which is exactly what Im suggesting we don't need to do. We can get almost everything we need just from the ordering structure: we don't need to get all tied up in distinguishing cases which can only be formally stated by using all the machinery of real analysis.
4. Pat argues that "I'm largely in agreement with Jixin about points and intervals, although I dont think its got anything to do with knowledge". But it does. In fact, as pointed out by Pat himself, "if you want to know whether the light was on or not, you have to say which interval you are talking about". In other words, if the (additional) knowledge of "which interval you are talking about" is given (e.g., in terms of which interval is open/closed at the switching point, or in terms of the corresponding meets relations  "knowledge"?), we can say whether the light was on or not. 
Again I was careless in using the word "knowledge", sorry. I should have said: in order to answer the question whether the light is on or off, one has to specify the interval with respect to which this question is posed. On this view, the truth or otherwise of a proposition is only meaningful with respect to certain intervals. I dont mean that the facts are determined by knowing more about the details of the interval, but that the question is a different question when asked about one interval than when asked about another, and for some intervals in may be simply meaningless. Is the light on or off at (exactly) 3.00 pm? The only way to answer this is to find a suitable nonpointlike interval of light or darkness completely surrounding 3.00 pm, because 'being on' is the kind of proposition that requires a nonpointlike reference interval.
This has nothing to do with whether an interval is open or closed: in fact, there is no such distinction in this theory. It only arises in a much more complicated extension which includes set theory and an extensionality axiom for intervals.
5. Pat also argues that his formulation is simpler (and elegant). In
what aspects, compared with which formulation?

It seems that it still
needs a lot of axioms to characterise the formal structure, especially
when issues such as density, linearity, boundness, etc, are to be
addressed.

The theory is basically linear in its nature, since it assumes timepoints are totally ordered. One can easily weaken it to allow partial orders, but then the extensions involving density, etc.,, get rather tricker. I think the universe is deterministic in any case, so linearity doesnt bother me :)
Pat Hayes
From: Ray Reiter on 29.3.1998
During all the years that the debate has raged about time points vs intervals, we devotees of the sitcalc have never seen it as an issue. Here's why I think this is so.
In the sitcalc, a fluent (
_{ } LightOn(do(switchOn, do(switchOff, S0))) 
_{ } ¬ LightOn(do(switchOff, do(switchOn, S0))) 
In the sitcalc with explicit time, the first might become
_{ } LightOn(do(switchOn(3.14), do(switchOff(1.41), S0))) 
meaning that as a result of the action history consisting of first
switching off the light at time 1.41, then switching on the light at time 3.14,
the light will be on. Notice that there is no way of expressing the claim that
the light is, or is not on at time 3.14 (or 3.5), independently of the
situation leading up to this time. On
the other hand, time based formalisms do allow one to write
Now, one could rightly object to the above account because it provides only for fluent truth values at discrete time points, namely at the action occurrence times. So we are tempted to understand
_{ } LightOn(do(switchOn(3.14), do(switchOff(1.41), S0))) 
to mean that the light is on at time 3.14, but it tells us nothing about time 3.5 say. This is particularly bad for (functional) fluents that vary continuously with time, for example, the location of a falling object. To handle this, introduce a time argument for fluents, in addition to their situation argument. For the light, one can write:
_{ } LightOnT(t, s) <> LightOn(s)_{ ^ }t > start(s). 
Here,
An instance of this would be
_{ } LightOnT(t, do(switchOn(3.14), do(switchOff(1.41), S0))) <> t > 3.14 
Here we have committed to the light being on at exactly the time of the switchOn action, and forever thereafter, relative to the history
_{ } do(switchOn(3.14), do(switchOff(1.41), S0)) 
_{ } LightOnT(3.14, do(switchOn(3.14), do(switchOff(1.41), S0))) 
_{ } ¬ LightOnT(3.14, do(switchOff(1.41), S0)) 
without contradiction. This seems to be precisely the point at which purely timebased formalisms run into difficulties, and the sitcalc version of this problem illustrates the role that explicit situation arguments play in resolving these difficulties.
Now, we can axiomatize falling objects:
_{ } positionT(t, s) = position(s)+  
_{ } velocity(s)*(tstart(s))+0.5*g*(tstart(s))^{2} 
From: John McCarthy on 29.3.1998
When my car accelerates, there is a time point at which it passes 65 miles per hour. It is awkward to describe this point in a language not providing for time points.
From: Graham White on 31.3.1998
John McCarthy wrote:
When my car accelerates, there is a time point at which it passes 65
miles per hour. It is awkward to describe this point in a language
not providing for time points.

Graham White
From: John McCarthy on 31.3.1998
McCarthy and Hayes (1969) used time as a fluent on situations, i.e. time(s). One motivation was that people, and perhaps future robots, often do not know the time with sufficient resolution to compare two situations, e.g. Ray Reiter's recent message with times 1.41 and 3.14. A second motivation for making situations primary was to make it correspond to human common sense. Many people who can reason about the consequences of actions in situations perfectly well do not know about real numbers, and some don't know about numbers at all. The falling body example was also in that paper with time as a fluent. Galileo did know about real numbers.
It's not clear that either of these considerations is of basic importance for AI.
My previous message gave a reason for including time points in a theory of events and actions. The theory could be founded so as to regard them as degenerate intervals, but I don't see any advantage in that, although I suppose the idea stems from the fact that people and robots can't measure time precisely.
From: Pat Hayes on 31.3.1998
Responses to Ray Reiter and John McCarthy. Ray wrote:
In the sitcalc, a fluent (
In the sitcalc with explicit time, the first might become
meaning that as a result of the action history consisting of first switching off the light at time 1.41, then switching on the light at time 3.14, the light will be on. Notice that there is no way of expressing the claim that the light is, or is not on at time 3.14 (or 3.5), independently of the situation leading up to this time. 
I think of Ray's 'sequences of actions' as alternative ways the temporal universe might be, ie possible timelines (or histories, as Ray sometimes calls them.) The point/interval controversy is about reasoning within, or with respect to, one of these possible timelines; sitcalc gets this muddled up with reasoning about alternative futures for the partial timeline up to the present. (Think of the tree of accessible situations in a state's future: the distinction is between reasoning about a single branch, and comparing two different branches.)
On the other hand, time based formalisms do allow one to write

Now, one could rightly object to the above account because it provides only for
fluent truth values at discrete time points, namely at the action occurrence
times. So we are tempted to understand
to mean that the light is on at time 3.14, but it tells us nothing about time 3.5 say. This is particularly bad for (functional) fluents that vary continuously with time, for example, the location of a falling object. To handle this, introduce a time argument for fluents, in addition to their situation argument. 
Hold on! What kinds of things are these 'times' supposed to be? They seem to be something like clocktimes, ie temporal coordinates (maybe understood with respect to a global clock of some kind.) OK, but notice that this isn't what I mean by a 'timepoint'. There are at least six distinct notions of 'time' (physical dimension, timeplenum, timeinterval, timepoint, timecoordinate and duration.) I think the nearest thing in Reiter's ontology to what I call a timepoint is something like the pairing of a clocktime with a situation ('3.14 in situation s').
For the light, one can write:
Here, An instance of this would be
Here we have committed to the light being on at exactly the time
of the
without contradiction... 
This seems to be the halfopeninterval solution, where intervals contain their endpoints but not their starting points. This makes sense for the sitcalc, which focusses on the results of actions, but seems adhoc and unintuitive in a broader context. (Also, BTW, the idea that one can ever say that some finite list of actions is all the actions that have occurred seems quite unrealistic. After all, people's fingers probably pushed the switch and something somewhere was generating electricity. Surely one should be able to actually infer this from a reasonably accurate commonsense description of lightswitching.)
...This seems to be precisely the point at which purely
timebased formalisms run into difficulties, and the sitcalc version
of this problem illustrates the role that explicit situation arguments
play in resolving these difficulties.

The problem is that even if we stick to talking about a single timeline (eg the unique past, or one alternative future) there still seems to be an intuitive difficulty about timepoints like the time when a light came on. The solution I suggested  that is, truth at a point has to be defined relative to a reference interval containing the point (which is not my idea, let me add)  is similar in many ways to Reiter's , except it applies not just across timelines but also within a single one.
John wrote:
When my car accelerates, there is a time point at which it passes 65
miles per hour. It is awkward to describe this point in a language
not providing for time points.

The 65mph example is logically similar to the point at the top of a
trajectory when the vertical velocity is zero. Examples like this appeal to
a basic intuition about continuous change, that it has no 'jumps', so if it
is
(continuous X i) =df (forall (y)(implies (between (X (begin i)) y (X (end y))) (exists t) (and (in t i) (= y (X t)))) (strictlycontinuous X i) =df (forall (j) (implies (subint j i)(continuous X j)))
where subint is the Allen union {begins, inside, ends}. (This assumes that the timeline itself is dense; if not, strictlycontinuous is trivially true everywhere.) Other conditions like monotonicity and so forth also transcribe directly from their usual mathematical formulations.
Pat Hayes
Workshop Discussions 
Eyal Amir
PointSensitive Circumscription
Peter Grünwald
Ramifications and sufficient causes