Re: RSP Telco 25.09 and ISWC/OrdRing

In today's discussion, Minh proposed that the partial order of 
timestamps in a stream be specified on a predicate-by-predicate basis, 
as a way to allow greater generality of streams while still preserving 
the ability to merge arbitrary streams. This is consistent with the 
requirement that ordering in the stream is only with respect to 
timestamps of the same predicate.

The mathematical requirements for a partial order (<=) of timestamps 
could be as follows:

1. The usual mathematical requirements of a partial order apply 
(http://mathworld.wolfram.com/PartialOrder.html):
a) Reflexivity X <= X
b) Antisymmetry X <= Y and Y <= X implies X = Y
c) Transitivity X <= Y and Y <= Z implies X <= Z

2. The partial order must respect the natural order of time.
In particular, if every time instant within the closure of temporal 
entity X is earlier than every time instant within the closure of 
temporal entity Y, then X <= Y
(where closure of a time instant t is defined as the degenerate interval 
[t, t], and closure of an interval is defined in the usual way)


I don't believe there is a need for any other conditions. I have phrased 
this to intentionally avoid specifying an ordering between a time 
instant t and the corresponding degenerate time interval [t, t], or 
between an open time interval (t_1, t_2) and its closure [t_1, t_2].

Tara

Received on Friday, 25 September 2015 14:37:49 UTC