Towards a general theory for modelling qualitative space

Qualitative spatial representation and reasoning are techniques for modeling and manipulating objects and relationships in space. Finding ways for defining the complete and sound (physically plausible) set of relationships between spatial objects is a prerequisite for the development and realization of qualitative representation and reasoning formalisms. Establishing the set of sound relationships is a complicated task especially when complex objects are considered. Hence, current approaches to qualitative representation and reasoning are limited to handling simple spatial objects. In this paper, we introduce a constraint-based approach to qualitative representation of topological relationships by defining a set of general soundness rules. The rules reduce the combinatorial set of relations produced by the method to the complete and physically possible ones. The rules are general and apply to objects of arbitrary complexity and together with the representation and reasoning formalism form a theory for qualitative space

Order in space: a general formalism for spatial reasoning

In this paper we propose a general approach for reasoning in space. The approach is composed of a set of two general constraints to govern the spatial relationships between objects in space, and two rules to propagate relationships between those objects. The approach is based on a novel representation of the topology of the space as a connected set of components using a structure called adjacency matrix which can capture the topology of objects of different complexity in any space dimension. The formalism is used to explain spatial compositions resulting in indefinite and definite relations and it is shown to be applicable to reasoning in the temporal domain. The main contribution of the formalism is that it provides means for constructing composition tables for objects with arbitrary complexity in any space dimension. A new composition table between spatial objects of different types is presented. A major advantage of the method is that reasoning between objects of any complexity can be achieved in a defined limited number of steps. Hence, the incorporation of spatial reasoning mechanisms in spatial information systems becomes possible

SPARQS: a qualitative spatial reasoning engine

In this paper the design and implementation of a general qualitative spatial reasoning engine (SPARQS) is presented. Qualitative treatment of information in large spatial databases is used to complement the quantitative approaches to managing those systems, in particular, it is used for the automatic derivation of implicit spatial relationships and in maintaining the integrity of the database. To be of practical use, composition tables of spatial relationships between different types of objects need to be developed and integrated in those systems. The automatic derivation of such tables is considered to be a major challenge to current reasoning approaches. In this paper, this issue is addressed and a new approach to the automatic derivation of composition tables is presented. The method is founded on a sound set-theoretical approach for the representation and reasoning over arbitrarily shaped objects in space. A reasoning engine tool, SPARQS, has been implemented to demonstrate the validity of the approach. The engine is composed of a basic graphical interface where composition tables between the most common types of spatial objects are built. An advanced interface is also provided, where users are able to describe shapes of arbitrary complexity and to derive the composition of chosen spatial relationships. Examples of the application of the method using different objects and different types of spatial relationships are presented and new composition tables are built using the reasoning engine

Episodes in space: qualitative representation and reasoning over spatio-temporal objects

There is growing interest in many application domains for the temporal treatment and manipulation of spatially referenced objects. Handling the time dimension in spatial databases can greatly enhance and extend their functionality and usability by offering means of understanding the spatial behaviour in time. Few works, to date, have been directed towards the development of formalisms for representation and reasoning in this domain. In this paper, a new approach is presented for the representation and reasoning over spatio-temporal relationships. The approach is simple and aims to satisfy the requirements of coherency, expressiveness and reasoning power. Consistent behaviours of spatial objects in time are denoted episodes. The topology of the domain is defined by decomposing episodes into representative components and relationships are defined between those components. Spatio-temporal reasoning is achieved by composing the relationships between the object components using constraint networks. New composition tables between simple spatio-temporal regions and between regions and volumes are also derived and used in the reasoning process

Qualitative representation and reasoning with uncertainty in space and time

Imprecision, indeterminacy and vagueness are all terms which have been studied recently in studies of representations of entities in space and time. The interest has arisen from the fact that in many cases, precise information about objects in space are not available. In this paper a study of spatial uncertainty is presented and extended to temporal uncertainty. Different types and modes of uncertainty are identified. A unified framework is presented for the representation and reasoning over uncertain qualitative domains. The method addresses some of the main limitations of the current approaches. It is shown to apply to different types of entities with arbitrary complexity with total or partial uncertainty. The approach is part of a comprehensive research program aimed at developing a unified complete theory for qualitative spatial and temporal domain

Qualitative tools to support visual querying in large spatial databases

In this paper a visual approach to querying in large spatial databases is presented. A diagrammatic technique utilising a data flow metaphor is used to express different kinds of spatial and non-spatial constraints. Basic filters are designed to represent the various types of queries in such systems. Icons for different types of spatial relations are used to denote the filters. Different granularities of the relations are presented in a hierarchical fashion when selecting the spatial constraints. The language constructs are presented and examples are used to demonstrate the expressiveness of the approach in representing different kinds of queries, including spatial joins and composite spatial queries. 1