Issue 98056 | Editor: Erik Sandewall | 14.7.1998 |
Today |
Today's newsletter contains the answer by Jixin Ma to Erik Sandewall's question yesterday in the discussion about the ontology of time, plus a question from Michael Thielscher to Marc Denecker, Daniele Theseider Dupré, and Kristof Van Belleghem, making it the third question for their ETAI submitted article.
ETAI Publications |
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.
Marc Denecker, Daniele Theseider Dupré, and Kristof Van Belleghem
An Inductive Definition Approach to Ramifications
Debates |
In ENRAC 11.7 (98054), Erik wrote:
I had actually asked for something more concrete: a scenario that can't
be expressed, or a scenario query that requires inordinately long
completion time, for example. Is it possible to be more specific about
in what sense it "will be more difficult" to represent time points that
stand between intervals?
|
As for the sense of "it will be difficult to represent time points in an appropriate structure so that they can stand between intervals conveniently", what I mean here is, if all time intervals are taken as semi-open and therefore they can sit next to one another, it would br difficult to allow time point to stand between intervals, since it is not appropriate to represent time points with the semi-open structure.
However, it seems that by some careful and proper treatments, we may
also reach the same results by defining the concepts of intervals
based on points. The key point here is, in addition to the concept of
lower and upper bounds for point-based intervals, the concept of left
type and right type for intervals needs to be addressed as well. What
follows is the skeleton of the structure:
|
Yes, but how does this differ from the standard notions of open and
closed intervals? It would appear that
(a,b,open,open) = (a,b) (a,b,open,close) = (a,b]and so on. Are there some models where your fourtuple intervals can not be reduced to standard definitions, such as (a,b) = {x | a < x < b}and so on? Do those "nonstandard" models have some interesting properties? |
First of all, in the quaternion form (p1, p2, l, r), the left-type,
l, and right-type, r, are allowed to be unspecified.
Therefore, without knowing what is the exactly value of r' and l'',
we can still have Meets((p1',p2',l',r'), (p1'',p2'',l'',r'')) if we
just have
Secondly, for general treatments, intervals don't necessarily have
to be sets of points, though they can be specified as such a model,
e.g., as Erik suggested,
In addition, both the point-based time theory using the quaternion structure, and the time theory that takes both intervals and points as primitive allow the expression of the case (case 4?) where a left-open interval Meets a point which, in turn, Meets a right-open interval (This open/closed nature would be expressed by the Meets relation when both intervals and points are taken as primitive).
What follows is an example of using the time model in modelling some critical problems:
Gelfond et al noted some of the limitations of the Situation
calculus, and specially proposed an approach to represent actions
with delayed effects. They use an action called
In fact, there are two
situations, one is the situation where the ball is at the stationary
point, another is the situation immediately after the stationary
point. Both of them satisfy that the
However, if we associate actions with "typelised" point-based intervals, we may sucessfully express them. For the former, the associated interval's right type is "open", i.e., excluding the stationary point; while for the latter, the associated interval's right type has to be "closed", i.e., including the stationary point. For both cases, the left type may be unknown.
Jixin