Issue 406: Question about quantification + transitivity + open world
Posted by Robert Sanderson on 2/2/2019
In considering whether the serialization of a property should be a single resource or an array, I of course looked to the quantification. However, I realized that the combination of transitivity and one:many quantification in the open world seems to produce unexpected results.
There are several transitive properties in the CRM, and the ones that matter most are the partitioning properties such as P9.
If a period A p9 consists of period B, and period B p9 consists of period C, then we can conclude via the stated transitivity of the property, that period A consists of both period B (by declaration) and period C (by inference from transitivity). However the quantification of P0 is one to many, not many to many and thus it seems like it is incorrect to assert that A p9 B, A p9 C.
Further, when considering the open world, there might be other identities for period B. Meaning that if period X is sameAs period B, then it is also valid to say that period A p9 period B, and period A p9 period X (because B == X).
Given these two second degree patterns, it seems like the quantification applies only in the abstract and does not need to be taken into account directly by implementations?
posted by Martin on 12/2/2019
Yes, indeed, we have a problem here. I do not think it is an Open World problem. At first, transitivity is incompatible with one-to-many.
That being said, the next question is, if the part decomposition must be a tree. I think this was the idea behind the quantification. That is a more complex constraint to be formulated. I.e., A p9 B, A p9 C => B P9 C OR C p9 B, or so
However, P9 is a very general parthood concept, which applies also to events, and not only to historical or archaeological periods, subdivided by scholars into phases and regional phases.
I assume that a particular action can quite well be seen to be part of two different "super"-events. This is an area of reasoning we have not yet explored well. Opinions?
In that case, we have to drop the tree constraint as well.
The property must not refer to itself (NOT A p9 A) and cycle-free, and improper parthood, i.e., A p9 B and B p9 A, you refer below, is not useful and should be forbidden. I believe a part must have a smaller extent than the whole, in order to be intuitively correct. I think we intend to support extensional parthood. This should be formulated via points in the respective space-time volumes.
By sure, the quantification as it stands is ontologically wrong, i.e., in the abstract already, as you pose it. It is not a question of implementing a system tolerable to knowledge alternatives.
Thank for spotting!