. The field of Qualitative Spatial Reasoning is now an active research area in its own right within AI (and also in Geographical Information Systems) having grown out of earlier work in philosophical logic and more general Qualitative Reasoning in AI. In this paper (which is an updated version of [25]) I will survey the state of the art in Qualitative Spatial Reasoning, covering representation and reasoning issues as well as pointing to some application areas. 1 What is Qualitative Reasoning? The principal goal of Qualitative Reasoning (QR) [129] is to represent not only our everyday commonsense knowledge about the physical world, but also the underlying abstractions used by engineers and scientists when they create quantitative models. Endowed with such knowledge, and appropriate reasoning methods, a computer could make predictions, diagnoses and explain the behaviour of physical systems in a qualitative manner, even when a precise quantitative description is not available 1 ...

This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned.

. Although Qualitative Reasoning has been a lively subfield of AI for many years now, it is only comparatively recently that substantial work has been done on qualitative spatial reasoning; this paper lays out a guide to the issues involved and surveys what has been achieved. The papers is generally informal and discursive, providing pointers to the literature where full technical details may be found. 1 What is Qualitative Reasoning? The principal goal of Qualitative Reasoning (QR) [86] is to represent not only our everyday commonsense knowledge about the physical world, but also the underlying abstractions used by engineers and scientists when they create quantitative models. Endowed with such knowledge, and appropriate reasoning methods, a computer could make predictions, diagnoses and explain the behaviour of physical systems in a qualitative manner, even when a precise quantitative description is not available 1 or is computationally intractable. The key to a qualitative ...

. This chapter surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned. 1. Introduction Qualitative Reasoning (QR) has now become a mature subfield of AI as its tenth annual international workshop, several books (e.g. (Weld and De Kleer 1990, Faltings and Struss 1992)) and a wealth of conference and journal publications testify. QR tries to make explicit our everyday commonsense kno...

This thesis investigates logical representations for describing and reasoning about spatial situations. Previously proposed theories of spatial regions are investigated in some detail --- especially the 1st-order theory of Randell, Cui and Cohn (1992). The difficulty of achieving effective automated reasoning with these systems is observed. A new approach is presented, based on encoding spatial relations in formulae of 0-order (`propositional ') logics. It is proved that entailment, which is valid according to the standard semantics for these logics, is also valid with respect to the spatial interpretation. Consequently, well-known mechanisms for propositional reasoning can be applied to spatial reasoning. Specific encodings of topological relations into both the modal logic S4 and the intuitionistic propositional calculus are given. The complexity of reasoning using the intuitionistic representation is examined and a procedure is presented which is shown to be of O(n 3 ) complexity ...

. Region Based Geometry (RBG) is an axiomatic theory of qualitative congurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and geometrical axioms involves set theory, in RBG the interface is achieved by purely 1st-order axioms. This means that the elementary sublanguage of RBG is extremely expressive, supporting inferences involving both mereological and geometrical concepts. Categoricity of the RBG axioms is proved: all models are isomorphic to a standard interpretation in terms of Cartesian spaces over R. 1. Introduction Many researchers in the eld of Qualitative Spatial Reasoning (QSR) have argued that it is useful to have representations in which spatial regions are the basic entities [10, 8]. This ontology contrasts with the approach of classical geometry, where lines, surfaces and regions are typically thought of as ...

We propose a strategy to decompose a polygon, containing zero or more holes, into “approximately convex” pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignore less significant artifacts such as wrinkles and surface texture. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant non-convex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of ‘increasingly convex ’ decompositions. A user specified tolerance determines the degree of concavity that will be allowed in the lowest level of the hierarchy. Our algorithm computes an ACD of a simple polygon with n vertices and r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard or, if the polygon has no holes, takes O(nr 2) time. Models and movies can be found on our web-pages at:

This paper attempts a survey of the computational modalities for representing spatial expressions. The focus is on computational or synthetic models, as opposed to cognitive or linguistic aspects. A number of formalisms based on qualitative paradigms such as topology seek to discretize space into regions based on alignment or tangency. This approach may be termed as "neat". Yet a large class of spatial expresssions (e.g. "near", "move away from") do not involve alignments, and even some which do (e.g. "in-front-of") have gradations. These gradations in a continuum are clearly less "neat"; we may view these as "scruffy"; there appears to be a growing trend towards the scruffy in recent times. The distinctions between the different models reviewed are demonstrated using the canonical example of "the chair in front of the desk". 1 Introduction The philosopher Wittgenstein, when young, (Tractatus, 1921), claimed to have provided a "final solution" to the problem of logic and la...

There is now a growing literature on qualitative spatial representations covering many aspects of spatial representation including mereology, topology, orientation and distance. In this paper I will briefly outline some of these approaches to qualitative spatial representation and then apply these theories to the task of formalising a non-trivial domain: that of representing cell structure. The paper is thus a contribution to the evaluation of qualitative spatial representations and spatial ontologies and may form the basis of a bio-informatic information system.

Abstract. How can the usability of distributed and heterogeneous geographic data sets be enhanced? Semantic interoperability is a prerequisite for effectively finding and accessing relevant data in different application contexts. By using geospatial domain ontologies and semantic annotations of geodata based on these ontologies semantic interoperability can be achieved. However, since no automated methods for the semantic annotation of geodata exist this remains a laborious task, which data providers are neither willing nor capable to perform. In this paper we propose a method for automating the annotation process based on spatial relations. At the domain level, spatial relations play an important role for defining and identifying geospatial concepts. At the data level, spatial relations may be expressed through spatial processing methods, as we can calculate relations like topology, direction or distance between two spatial entities. We show how this potential can be exploited for automating the semantic annotation of geodata. The approach is illustrated by introducing a case study for annotating data containing representations of floodplains. 1