Spatiotemporal overlaps of periods

or spatiotemporal relationships:
It has been proposed to use only the following two spatiotemporal relationships. 
Period - "overlaps with: Period", "falls within : Period" (existing)
This choice should be further justified. 

In Paris I was ask to explain my position with respect to the spatiotemporal overlaps of periods. I
propose to use except for the part-whole relation and the inclusion only one more purely spatiotemporal
relationship:
"overlaps".

Here my view:
If we declare a property in the CRM, it should be clearly defined and clearly needed for the purpose
of the CRM both in functionality and in frequency of use.

From a mathematical point of view, all topological relationships can be derived from the inclusion. This may in practice be quite clumsy: E.g. in order to define an overlap we have to include the common part by both entities. So we have to define somehow artificially the overlapping part etc. So one argument is to introduce additional relationships for convenience.

Now, Periods extend over a 4-dimensional space. Such a space has no complete order, and arbitrary directions in time-space like the flight of a plane have few cultural relevance - i.e. we shall hardly find a documentation with enough data to decribe it precisely. Equally unlikely is the chance, to compare such data with others for reasoning, e.g. when the plane crashed into the building. More likely, we shall find documented relationships restricting overall time or place or both. So another argument is the complexity to handle relationships in multiple dimensions and the probability tofind data for them.

Finally, the purpose of the CRM is to facilitate resource discovery by precise descriptions. More specialized relationships can be replaced by simpler ones, which preserve recall. E.g. instead of seeking the plane that crossed Halifax at 16:00, I can search for planes on the route over Halifax within +/- 8 hours. This will return more planes than I needed, but it will include the candidates.

Temporal bounds are typically rich and with good precision in cultural documentation. The fact, that time is one-dimensional makes comparison easy. Therefore we have already decided on the relatively rich temporal relationships by Allen, which can be regarded as a standard in Knowledge Representation and are well studied and well-understood:

before (after) : E2 Temporal Entity
meets in time (met-by in time): E2 Temporal Entity
overlaps in time (overlapped-by in time): E2 Temporal Entity
during (includes): E2 Temporal Entity
starts (started-by): E2 Temporal Entity
finishes (finished-by): E2 Temporal Entity
equal in time: E2 Temporal Entity

All those are also available for Periods to describe the extent in time via inheritance.

Spatial relationships already deal with 2 or 3 dimensions. We have decided in Paris to use:
E53 Place - "borders with: E53 Place", "overlaps with: E53 Place".

Those have a high frequency in our data. Countries etc. have borders, modern districts may overlap with ancient ones etc. Reasoning and retrieval based on these is straightforward. One could introduce direction, like "north of" , distances etc. Reasoning and retrieval of such data exceeds the capabilities of usual applications. Of course GIS can deal with that. On the other side, if I look for some places being "north of" a known one, I can determine the area by hand and post a query on that base. Therefore we have decided in Paris, that the above spatial relationships together with inclusion are sufficient and appropriate for the CRM.

These spatial relationships are available to describe related periods. Hence, Periods can be restricted in time and in space by the above relationships. What else do we need?

As Periods can spread out over time and space in a "non-rectangular shape", i.e. not constant for a certain time-span at some spatial borders, even two Periods in the same time and space "box" need not overlap. Let us think for instance of some fashion movement coming from the US to Europe, and before it ends in Europe, another movement in the US has already taken over. A purely spatiotemporal overlap, which cannot be decomposed into spatial and temporal overlaps, is relatively rare, but difficult to be described
otherwise. It is also culturally relevant, because we can fairly assume mutual influences, or wonder why these periods behave independently.

Therefore I have proposed to include the pure spatiotemporal overlap as relationship for the CRM. All other purely spatiotemporal relationships I regard as too complex for a standard.

I could only imagine one more relevant relationship between Periods: "follows". Imagine a situation as with the fashion movement above. There is no overall temporal sequence, but at any individual place, the second period "follows (is followed by)" the first. This would be a complement to the spatial "borders with", and a refinement of the temporal "meets", relative to the various points in the respective area a period is active.

MD, January 2002.