Recent research has identified rule learning as a promising technique for geographic pattern mining and knowledge discovery to make sense of the big spatial data avalanche (Koperski & Han, 1995; Shekhar et al., 2003). Rules conveying associative implications regarding locations, as well as semantic and spatial characteristics of analyzed spatial features, are especially of interest. This overview considers fundamentals and recent advancements in two approaches applied on spatial data: spatial association rule learning and co-location rule learning.

Scale and generalization are two fundamental, related concepts in geospatial data. Scale has multiple meanings depending on context, both within geographic information science and in other disciplines. Typically it refers to relative proportions between objects in the real world and their representations. Generalization is the act of modifying detail, usually reducing it, in geospatial data. It is often driven by a need to represent data at coarsened resolution, being typically a consequence of reducing representation scale. Multiple computations and graphical modication processes can be used to achieve generalization, each introducing increased abstraction to the data, its symbolization, or both.

Basic mathematical set theory is presented and illustrated with a few examples from GIS. The focus is on set theory first, with subsequent interpretation in some GIS contexts ranging from story maps to municipal planning to language use. The breadth of interpretation represents not only the foundational universality of set theory within the broad realm of GIS but is also reflective of set theory's fundamental role in mathematics and its numerous applications. Beyond the conventional, the reader is taken to see glimpses of set theory not commonly experienced in the world of GIS and asked to imagine where else they might apply. Initial broad exposure leaves room for the mind to grow into deep and rich fields flung far across the globe of academia. Direction toward such paths is offered within the text and in additional resources, all designed to broaden the horizons of the open-minded reader.

Advances in computational capacity have enabled dynamic simulation modeling to become increasingly widespread in scientific research. As opposed to conceptual or physical models, simulation models enable numerical experimentation with alternative parametric assumptions for a given model design. Numerous design choices are made in model development that involve continuous or discrete representations of time and space. Simulation modeling approaches include system dynamics, discrete event simulation, agent-based modeling, and multi-method modeling. The model development process involves a shift from qualitative design to quantitative analysis upon implementation of a model in a computer program or software platform. Upon implementation, model analysis is performed through rigorous experimentation to test how model structure produces simulated patterns of behavior over time and space. Validation of a model through correspondence of simulated results with observed behavior facilitates its use as an analytical tool for evaluating strategies and policies that would alter system behavior.