On 25 November 2010 10:54, Jakob Voss <[log in to unmask]> wrote:
Edward C. Zimmermann wrote:

We have time intervals (5.5) and Recurring time-intervals (5.6)

Thanks. At "4.1 Basic concepts" the specification says "three concepts are fundamental:" to list four concepts afterwards. :-) I'll skipp recurring time-intervals for simplicity. So there is (citing the specification):

1. Time-point: instant in the laps of time regarded as dimensionless

Examples of simple time-points are dates.

2. Time-interval: a portion of time between two time-points.

A time-interval is one of
- a start and an end
- a duration not associated with any start or end
- a start and a duration
- a duration and an end

As I read the specification, a "start" or "end" is an instance of a time-point. Time intervals and Time points can be compared by the method "inside of".

Thanks for this useful summary -- I don't see anything controversial here at all.
We now extend this model by introducing:

3. Time-collection: a set of time-points and/or time-intervals.

4. Time-choice: One of
- a time-collection, that one unknown element is selected from
- a time-interval, that one unknown time-interval or time-point is selected from

5. Approximate times: A time-point, time-interval, or time-collection marked as approximate.

6. Questionable times: A time-point, time-interval, time-collection, or approximate time marked as approximate.

To me, it would be helpful to thin this out a bit, and start by firming up on the different concepts of uncertainty, approximation, and questionableness of a single value. As they are all forms of *not* knowing a precise value, I would suggest starting with a minimalist idea of what the distinctions are. That is, it would be best not to assume distinctions of types of lack of knowledge unless there are convincing reasons for asserting them.

Using what knowledge and experience I have of mathematics, physics, philosophy of science and logic,  at present there appear to me relevantly three usefully different variants of uncertainty of a discrete value.

A. A best guess. "I have followed my own procedures for estimating the value, but I have no basis for a principled claim on what the error in this might be." This seems to correspond roughly with Jakob's "Questionable" for points. I do agree that sometimes possible error is not reasonably estimable.

B. A statistical estimate. "According to my calculations, the true value is probably around here, and I am confident (to which I can put a number and an estimation method) that the true value probably (with given probability) lies in this interval." This hasn't been suggested, and I don't know whether people would find it helpful. However, it certainly is very common within scientific disciplines, and has relevant application to dates in, e.g. radiocarbon dating.

C. Alternatives. "I have reason to believe that the true value
(i) is a point in this interval, or in this set of intervals
(ii) is one of this set of discrete values
(iii) some combination of (i) or (ii)."
I can easily imagine evidence for (i) or (ii), but I find (iii) more difficult to imagine in practice.
This looks similar to Jakob's "Time-collection", though I see it just as a construct to select a value from, as one can in principle select a single value from a set or from an interval.

On the other hand, one cannot select an interval from a set of point values. So an uncertain interval would have to be represented in one of just two ways
X: the interval between two uncertain point value times
Y: one of a set of intervals.

I think I have roughly the same amount of complexity as Jakob has represented here, but done differently.

I do think it is worth getting consensus here, clearly, before deciding how to represent the agreed concepts.

Simon Grant
+44 7710031657