We (Simon Scheider, Ben Gräler, Christoph Stasch, Edzer Pebesma) submitted a new paper, which presents a generative algebra for spatio-temporal information. You can download it from Simon’s website, here
Abstract: Maintaining knowledge about the provenance of data, i.e., about how it was obtained, is crucial for its further use. Contrary to what the overused metaphors of “data mining” and “big data” are implying, it is hardly possible to use data in a meaningful way if information about its sources and types of conversions are discarded in the process of data gathering. A generative model of data derivation could not only help automating the description of derivation processes, but also assessing the scope of a dataset’s future use by exploring possible transformations. Even though there are technical approaches to document data provenance, we still lack models for describing how spatio-temporal data is generated. To fill this gap, we introduce an algebra that models data generation and describes how data is derived, in terms of types of reference systems. We illustrate its versatility by applying it to a number of derivation scenarios, including trajectory generation and field aggregation, and discuss its potential for data recommendation, retrieval, as well as assessing the space of meaningful computations.
See Theories and Tools for the Isabelle/HOL theory that comes with it.