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. Chr-E ________________________________ From: Crm-sig <[email protected]> on behalf of Maximilian Schich <[email protected]> Sent: 13 October 2019 17:33 To: [email protected] 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:[email protected]?subject=[Appointment]> www.schich.info<http://www.schich.info/> 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? Best, Martin 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. Best, Christian-Emil _______________________________________________ Crm-sig mailing list [email protected]<mailto:[email protected]> http://lists.ics.forth.gr/mailman/listinfo/crm-sig -- ------------------------------------ Dr. Martin Doerr Honorary Head of the Center for Cultural Informatics Information Systems Laboratory Institute of Computer Science Foundation for Research and Technology - Hellas (FORTH) N.Plastira 100, Vassilika Vouton, GR70013 Heraklion,Crete,Greece Vox:+30(2810)391625 Email: [email protected]<mailto:[email protected]> Web-site: http://www.ics.forth.gr/isl _______________________________________________ Crm-sig mailing list [email protected]<mailto:[email protected]> http://lists.ics.forth.gr/mailman/listinfo/crm-sig
