We determine the implicit assumptions and the structure of the Single and Double Cross Calculi within Euclidean geometry, and use these results to guide the construction of analogous calculi in mereogeometry.  The systems thus obtained have strong semantic and deductive similarities with the Euclidean-based Cross Calculi although they rely on a different geometry. This fact suggests that putting too much emphasis on usual classification of qualitative spaces may hide important commonalities among spaces living in different classes.

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from both calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning (QSR), the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. Although CDC is more expressive than RA, reasoning with CDC is of the same order as reasoning with RA. We show that reasoning with basic RCC8 and basic RA relations is in P, but reasoning with basic RCC8 and basic CDC relations is NP-Complete.

Qualitative techniques for spatial reasoning are important in artificial intelligence. We present an extended cardinal direction calculus (XCDC) for spatio-temporal event representation and reasoning. The methods presented in this paper can be used in systems based on natural language processing which are also discussed in this paper.

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and `computational realisability' within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP- or PSPACE-complete.

Given an N N grid of squares, where each square has a count and an underlying population, our goal is to find the square region with the highest density, and to calculate its significance by randomization. Any density measure D, dependent on the total count and total population of a region, can be used. For example, if each count represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D

Given an N N grid of squares, where each square has a count and an underlying population, our goal is to find the square region with the highest density, and to calculate its significance by randomization. Any density measure D, dependent on the total count and total population of a region, can be used. For example, if each count represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D

Given an N N grid of squares, where each square has a count and an underlying population,our goal is to find the square region with the highest density, and to calculate its significance by randomization. Any density measure D, dependent on the total count and total population of a region, canbe used. For example, if each count represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D

Sketch maps are an important spatial representation used in many geospatial-reasoning tasks. This article describes techniques we have developed that enable software to perform humanlike reasoning about sketch maps. We illustrate the utility of these techniques in the context of nuSketch Battlespace, a research system that has been successfully used in a variety of experiments. After an overview of the nuSketch approach and nuSketch Battlespace, we outline the representations of glyphs and sketches and the nuSketch spatial reasoning architecture.

Sketch maps are an important spatial representation used in many geospatial-reasoning tasks. This article describes techniques we have developed that enable software to perform humanlike reasoning about sketch maps. We illustrate the utility of these techniques in the context of nuSketch Battlespace, a research system that has been successfully used in a variety of experiments. After an overview of the nuSketch approach and nuSketch Battlespace, we outline the representations of glyphs and sketches and the nuSketch spatial reasoning architecture. We describe the use of qualitative topology and Voronoi diagrams to construct spatial representations, and explain how these facilities are combined with analogical reasoning to provide a simple form of enemy intent hypothesis generation.

Reasoning about spatial data is a key task in many applications, including geographic information systems, meteorological and fluid-flow analysis, computer-aided design, and protein structure databases. Qualitative spatial reasoning (QSR) provides representational primitives (a spatial "vocabulary") and inference mechanisms for these tasks. It then turns to the data-rich case, where the goal is to derive and manipulate qualitative spatial representations that efficiently and correctly abstract important spatial aspects of the underlying data for use in subsequent tasks. This article focuses on how a particular QSR system, SPATIAL AGGREGATION, can help answer spatial queries for scientific and engineering data sets.