Dear Robert,
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!:-)
Best,
martin
On 2/2/2019 2:17 AM, Robert Sanderson wrote:
Dear all,
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?
Rob
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Dr. Martin Doerr
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Center for Cultural Informatics
Information Systems Laboratory
Institute of Computer Science
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