Issue 406: Question about quantification + transitivity + open world

Starting Date: 
Working Group: 

Posted by Robert Sanderson on 2/2/2019

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?

Current Proposal: 

posted by Martin on 12/2/2019

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!

Posted by Christian Emil on 13/10/2019

Dear all,

I work my way through all the open issues. This issue origins from an observation by Robert Sanderson that P9 cannot hav ethe cardinality 1 to many and at the same time be transitive. This is correct and will apply to all transitive properties. A transitive property will always be many to many. 
Have to be adjusted:

P5, P9, P10,   P73
Already many to many

P69 ok,​P86 ok, P89 ok, P114 ok, P115 ok, P116 ok, P117 ok, P120 ok, P127 ok, P139 ok, P148 ok, P150 ok, P165 ok
This is just editorial changes and need no discussion.

Posted by Martin on 13/10/2019

Dear Christian-Emil,

This is good. There is also another concern that in general parts can be shared by more than one whole. I would, nevertheless, add the constraint that part-of semantics mean also non-cyclic, wherever it applies. Could you check that?

Posted by Maximilian Schich  on 13/10/2019

One take-home from large-scale data-integration & data science is that even the strongest assumed 1-to-many relationship in reality is quasi-1-to-many due to differences in opinion (your tree vs. my tree), differences in construction of strong-tree classification systems (e.g. material/construction-method vs. construction-method/material in architecture), and differences in data preservation (cf. the integration of several strong-tree phylogenies based on different knowledge of the fossil record). As a consequence it would make good sense to model part-of relationships by default to allow for many-to-many at least as an exception, even if the ideal is 1-to-many for one reason or another.
Regarding this issue of "part-of as many-to-many", there is a crucial difference between more controlled data collections for "data reasoning" and a more realistic "data archaeology" that acknowledges the existing multiplicity of opinion. In the case of "data reasoning" many-to-many may be a computational hurdle. Yet in the case of "data archaeology" forced 1-to-many relationships are evil, as they induce an artificial discreteness in the data, very similar to the artificial yet often conceptually enforced discreteness of races, gender, etc. In this sense an artificial restriction of part-of semantics to 1-to-many relationships may be a potential source of severe systematic bias that needs to be avoided under all cost.
Consequently, there should be an emphasis on "general parts can be shared by more than one whole", particularly when facing heterogeneous sources of data. At the same time the audience should be provided with an explicit explanation why "non-cyclic, wherever it applies" could be a desire, while always accompanied by a caveat that "wherever it applies" may be true in considerable less cases than intuition would suggest.



Posted by Christian Emil on 13/10/2019

This is indeed an important discussion.  
My point is the formalist view.  If we have a set with a linear, transitive ordering like < for the integers, then this will be many to many under  the transitive closure. Assume a partial ordering without cycles: When we add transitivity the tree structure will still be there. If we store all pair resulting from the  transitive closure the tree structure is not explicit and has to be deduced form the set of pair. Take the whole part relationship: To make the tree structure explicit, we need a 1 to many cardinality. The fact a R b & b R c -> a R C has to be deduced.  If we instead are interested in the transitive closure to speed up deduction in an implementation the cardinality will be many to many.

Posted by Martin on 13/10/2019

Dear All,

I believe we need a many to many relation in any case, because the decision of a part can be further decomposed or not is often arbitrary,  things like buildings use to share parts, and parts may be exchanged, so that we are fooled by the "former or current" problem we cannot avoid. That part-of is a-cyclic should hold, I hope...