[Crm-sig] Issue 406: Question about quantification + transitivity + open world

Christian-Emil Smith Ore c.e.s.ore at iln.uio.no
Sun Oct 13 21:20:10 EEST 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.


From: Crm-sig <crm-sig-bounces at ics.forth.gr> on behalf of Maximilian Schich <maximilian at schich.info>
Sent: 13 October 2019 17:33
To: crm-sig at ics.forth.gr
Subject: Re: [Crm-sig] Issue 406: Question about quantification + transitivity + open world

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.

Best, Max

Dr. Maximilian Schich
Associate Professor, The University of Texas at Dallas, ATEC<http://www.utdallas.edu/atec/> & EODIAH<https://www.utdallas.edu/arthistory/>
800 W Campbell Rd AT10, Richardson TX 75080
Appointments via email<mailto:maximilian.schich at utdallas.edu?subject=[Appointment]>

On 2019-10-13 04:26, Martin Doerr wrote:
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?



On 10/13/2019 8:42 AM, Christian-Emil Smith Ore wrote:

​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.



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