Issue 98064 | Editor: Erik Sandewall | 20.8.1998 |
Today |
The discussion between Eugenia Ternovskaia and the authors Marc Denecker, Daniele Theseider Dupré, and Kristof Van Belleghem continues. It has proceeded as follows:
11.7 Eugenia 17.7 The authors 27.7 Eugenia 5.8 The authors 20.8 EugeniaFor those who have not followed the discussion in detail, an important part of it (especially in the latter messages) has concerned the relationship between causal rules and state constraints, which provide two different perspectives on ramification. One specific issue has been whether a causal rule involving more than one successor state is to be interpreted as a state constraint. -- The most recent contribution to the discussion follows below.
In the debate about the ontologis of time, Erik Sandewall today answers to Jixin Ma's contribution from 31.7 on that topic.
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 |
Dear Jixin,
In ENRAC 27.7 (98059) I wrote and you answered:
... the timepoint domain will then be agent-specific. It will also
be local to each scenario, ... In fact, it even becomes necessary
to revise the timepoint domain each time a query is asked...
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First of all, it is important to note that, by taking both intervals
and points as primitive, the time domain is general enough for various
scenarios, ... All these four cases are allowed by the same time
theory, without the need to revise the time domain at all.
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Now to the examples. I will take for granted that we talk about timepoints and intervals that are related along the lines of Pat's core theory, only with the adjustment that intervals are not entirely determined by their endpoints: there can be up to four intervals for each pair of endpoints, because you allow these intervals to be either open or closed at each end. (The interval will then be defined as closed if there exists a point beginning resp. ending it, otherwise it's open).
You refer to an example by Galton where a Green light and a Red light both switch On at the same time. This is somewhat counterintuitive - I would have thought that one goes Off when the other one goes On - but that doesn't matter. You propose the following scenario description for the case where we have decided to consider the Green light to be On at the dividing instant, and we have decided to keep that open for the Red light:
Holds(GreenOff, I2) Holds(GreenOn, P) Holds(GreenOn, J2) Holds(RedOff, I1) Holds(RedOn, J1) Meets(I2,P) Meets(P,J2) Meets(I1,J1) I1 + J1 = I2 + P + J2 |
My two examples come out in similar ways. For example A, you write:
Yeah, for the modelling of the throwing of a ball, it requires that
there exists a point referring to the apex. However, the fact that
Jim turned the switch does not necessarily imply that there must not
be any such point, especially if one insists that "at a moment (point?)
when it (the ball) reaches the top of its trajectory, he (Jim) turns
the switch".
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For example B, you write:
I don't agree with the claim that "a point both exists and does not
exist at the clocktime whent he winner finishes his last cone and the
bell rings". Again, I think this claim was reached by means of
confusing two cases, that is, the case that an interval "Meets" a
point, and the case that an interval was "Finished-by" a point.
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The bottom line is, therefore, that it is futile to try to impose noncommitment for dividing instants on the level of the models and by using nonstandard time domains such as "punctuated time". In those cases where we wish to express that we don't know or don't care whether a certain proposition is true or false at a point of change, it's sufficient to use the multiple models approach while admitting "standard" time (integers or reals, by preference). Then we don't need any theory of time at all besides high-school or (at most) college math.
All of this presumes of course standard two-valued logic, where models can only assign the truth-value true or false. You may obtain another perspective by going to e.g. three-valued logic, where everything can be undetermined besides true or false. But, as H.C. Andersen once said, that is another story.