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Ryan Wisnesky (Dec 21 2020 at 01:12):Would anyone be interested in working with myself and David Spivak to investigate "the data required to implement universal properties of functorial data migration (limits and co-limits of co-pre-sheaves as well as change-of-basis functors)" with respect to existing notions of lineage and provenance from database theory? Basically, to connect https://arxiv.org/abs/1212.5303 and https://courses.cs.washington.edu/courses/cse544/12sp/lectures/lecture18-provenance.pdf ? We think there's probably a paper in it and that it would be appropriate for jr grad students on up.
Henry Story (Dec 21 2020 at 09:47):Provenance is a very interesting topic and intuitively related to RDF Quads. I am happy to help along, and keen to use the results of the research. Intuitively provenance moves one to the space of what in philosophy is known as Speech Acts, and as I understand Linear Logic may be a way to encode those.
Joshua Meyers (Dec 21 2020 at 21:40):@Chao-Hong Chen
Henry Story (Dec 22 2020 at 22:25):Btw. the Semantic Web references for Provenance are:
Ryan Wisnesky (Jan 03 2021 at 07:17):To elaborate, when you implement the various constructions of functorial data migration using relational algebra and a key-generator, you have to keep around various tables in order to be able to construct the mediating morphisms required of the universal property. For example, associated with the relational algebra implementation of the "pi" functor (right adjoint to the model reduct functor) is an intermediate table whose schema is a comma category defined in terms of the input schema. To construct mediating morphisms involves querying this table. Moreover, we can use the mediating morphism to answer certain kinds of provenance queries. So, the basic idea behind this research is to understand the information encoded in these temporary tables, and connect it to database theory.