The next generation of Geographic Information Systems (GIS) is anticipated to automate some of the reasoning required for spatial analysis. An important step in the development of such systems is to gain a better understanding and corresponding modeling practice of when to apply arithmetic operations to quantities. The concept of extensivity plays an essential role in determining when quantities can be aggregated by summing them, and when this is not possible. This is of particular importance to geographic information systems, which serve to quantify phenomena across space and time. However, currently, multiple contrasting definitions of extensivity exist, and none of these suffice for handling the different practical cases occurring in geographic information. As a result, analysts predominantly rely on intuition and ad hoc reasoning to determine whether two quantities are additive. In this paper, we present a novel approach to formalizing the concept of extensivity. Though our notion as such is not restricted to quantifications occurring within geographic information, it is particularly useful for this purpose. Following the idea of spatio-temporal controls by Sinton, we define extensivity as a property of measurements of quantities with respect to a controlling quantity, such that a sum of the latter implies a sum of the former. In our algebraic definition of amounts and other quantities, we do away with some of the constraints that limit the usability of older approaches. By treating extensivity as a relation between amounts and other types of quantities, our definition offers the flexibility to relate a quantity to many domains of interest. We show how this new notion of extensivity can be used to classify the kinds of amounts in various examples of geographic information.

Transformations are essential for dealing with geographic information. They are involved not only in converting between geodata formats and reference systems, but also in turning geodata into useful information according to some purpose. However, since a transformation can be implemented in various formats and tools, its function and purpose usually remains hidden underneath the technicalities of a workflow. To automate geographic information procedures, we therefore need to model the transformations implemented by workflows on a conceptual level, as a form of procedural knowledge. Although core concepts of spatial information provide a useful level of description in this respect, we currently lack a model for the space of possible transformations between such concepts. In this article, we present the algebra of core concept transformations (CCT). It consists of a type hierarchy which models core concepts as relations, and a set of basic transformations described in terms of function signatures that use such types. Type inference allows us to enrich GIS workflows with abstract machine-readable metadata, by compiling algebraic tool descriptions. This allows us to automatically infer goal concepts across workflows and to query over such concepts across raster and vector implementations. We evaluate the algebra over a set of expert GIS workflows taken from online tutorials.

Abstract. There is an increasing trend of applying AIbased automated methods to geoscience problems. An important example is a geographic question answering (geoQA) focused on answer generation via GIS workflows rather than retrieval of a factual answer. However, a representative question corpus is necessary for developing, testing, and validating such generative geoQA systems. We compare five manually constructed geographical question corpora, GeoAnQu, Giki, GeoCLEF, GeoQuestions201, and Geoquery, by applying a conceptual transformation parser. The parser infers geo-analytical concepts and their transformations from a geographical question, akin to an abstract GIS workflow. Transformations thus represent the complexity of geo-analytical operations necessary to answer a question. By estimating the variety of concepts and the number of transformations for each corpus, the five corpora can be compared on the level of geo-analytical complexity, which cannot be done with purely NLP-based methods. Results indicate that the questions in GeoAnQu, which were compiled from GIS literature, require a higher number as well as more diverse geo-analytical operations than questions from the four other corpora. Furthermore, constructing a corpus with a sufficient representation (including GIS) may require an approach targeting a uniquely qualified group of users as a source. In contrast, sampling questions from large-scale online repositories like Google, Microsoft, and Yahoo may not provide the quality necessary for testing generative geoQA systems.