The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33, 34].

We present a logical theory of space where only tridimensional regions are assumed in the domain. Three distinct primitives are used to describe their mereological, topological and morphological properties: mereology is described by a parthood relation satisfying the axioms of Closed Extensional Mereology; topology is described by means of a "simple region" predicate, by which a relation of “strong connection ” between regions having at least a surface in common is defined; morphology is described by means of a "congruence " primitive, whose axioms exploit Tarski's analogy between points and spheres. 1

Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotopological reasoning in 2-dimensional space. Our strategy is to define a mereotopological language together with a familiar, point-based interpretation. It is proposed that, to be practically useful, any alternative region-based spatial ontology must support the same sentences in our language as this familiar interpretation. This proposal has the merit of transforming a vague, open-ended question about ontologies for "practical" mereotopological reasoning into a precise question in model theory. We show that (a version of) the familiar interpretation is countable and atomic, and therefore prime. We conclude that useful alternative ontologies of the plane are, if anything, less parsimonious than the one which they are supposed to replace.

The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science

We discuss an approach to a theory of physical objects and present a logical theory based on a fundamental distinction between objects and their substrates, i.e. chunks of matter and regions of space. The purpose is to establish the basis of a general ontology of space, matter and physical objects for the domain of mechanical artifacts. An extensional mereological framework is assumed for substrates, whereas physical objects are allowed to change their spatial and material substrate while keeping their identity. Besides the parthood relation, simple self-connected region and congruence (or sphere) are adopted as primitives for the description of space. Only threedimensional regions are assumed in the domain. This paper is a revision and slight modification of [Borgo et al. 1996]. 1.

We provide a model-theoretic framework for investigating and comparing a variety of mereotopological theories with respect to (i) the intended interpretation of their connection primitives, and (ii) the composition of their intended domains (e.g., whether or not they allow for boundary elements).

When modelling a domain, it is often the case that certain individuals are represented as belonging to multiple categories, generating therefore "tangled " hierarchies: 1. A physical object can be seen as an amount of matter 2. A hole can be seen as a region of space

To fix the semantics of different kinds of parthood relations we require axioms which go beyond those characterizing partial orderings. I formulate such axioms and show their implications for bio-ontologies. Specifically, I discuss parthood relations among masses, for example among body substances such as blood and portions thereof, and among components of complexes, for example between your stomach and your gastro-intestinal system. I contrast these with the relation of being contained in (as your lungs are contained in your thorax).

this paper as mappings between at objects of dierent kind. We show that vagueness in the denition of at objects involved in this process results in indeterminacy of location of those objects. Denitorial vagueness and location indeterminacy of location result in uncertainty about the truth of conclusions about existence, properties, and location of objects in the world derived from knowledge about at objects created by spatial analysis.

. This paper provides an ontological analysis of built environments. It shows that boundaries are ontologically salient features of built environments and that there are different kinds of boundaries that that need to be considered. It discusses in particular the important role of fiat boundaries. At the level of objects built environments are formed by partition forming objects and populated by non-partition forming objects. The underlying partition structure is the main organizational structure of a built environment. Non-partition forming objects are potentially movable and their movement is constrained by the barrier properties of the boundaries of other objects forming or populating the environment. This paper argues that the qualitative formalization of built environments needs to take into account: (1) the fundamental role of boundaries, (2) the distinction between bona-fide and fiat boundaries and objects, (3) the different character of constraints on relations betwe...