We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its useful expressiveness. An axiomatisation of the new theory and a comparison with the two original theories is given.

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].

Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the semantics of natural language expressions concerning locations and relative positions. While several authors have proposed axioms for these notions, no one with the exception of Tarski [18], who based his axiomatization of mereological notions on a Euclidean metric, has attempted to give them a semantics. We offer an alternative to Tarski, starting with mereotopological notions that have proved useful in the semantic analysis of spatial expressions. We also give a complete axiomatization of this account of mereotopological reasoning. 1

INTRODUCTION This is a brief overview of formal theories concerned with the study of the notions of (and the relations between) parts and wholes. The guiding idea is that we can distinguish between a theory of parthood (mereology) and a theory of wholeness (holology, which is essentially afforded by topology), and the main question examined is how these two theories can be combined to obtain a unified theory of parts and wholes. We examine various non-equivalent ways of pursuing this task, mainly with reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) theories; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory subsuming mereology. This is done in Sections 4 through 6. We also consider some more speculative strategies and directions for further research. First, however, we begin with some preliminary outline of

. This paper develops a taxonomy of qualitative spatial relations for pairs of regions, which are all logically defined from two primitive (but axiomatised) notions. The first primitive is the notion of two regions being connected, which allows eight jointly exhaustive and pairwise disjoint relations to be defined. The second primitive is the convex hull of a region which allows many more relations to be defined. We also consider the development of the useful notions of composition tables for the defined relations and networks specifying continuous transitions between pairs of regions. We conclude by discussing what kind of criteria to apply when deciding how fine a taxonomy to create. 3 The support of the SERC under grant no. GR/G36852 and GR/H 78955 is gratefully acknowledged. Thanks are also due to Brandon Bennett, John Gooday and Nick Gotts for useful comments. y Randell is now at the Dental School, Birmingham and Cui is now at ICRF, London. 0 1 Introduction Although the us...

This paper presents a formal theory for reasoning about motion of spatial entities, in a qualitative framework. Taking over a theory intended for spatial entities, we enrich it to achieve a theory whose intended models are spatio-temporal entities, an idea sometimes proposed by philosophers or AI authors but never fully exploited. We show what kind of properties usually assumed as desirable parts of any space-time theory are recovered from our model, thus giving a sound theoretical basis for a natural, qualitative representation of motion.

this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science fiction writers, and were of vital concern to our everyday life and commonsense reasoning. So whatever approach to AI one takes [ Russell and Norvig, 1995 ] , temporal and spatial representation and reasoning will always be among its most important ingredients (cf. [ Hayes, 1985 ] ). Knowledge representation (KR) has been quite successful in dealing separately with both time and space. The spectrum of formalisms in use ranges from relatively simple temporal and spatial databases, in which data are indexed by temporal and/or spatial parameters (see e.g. [ Srefik, 1995; Worboys, 1995 ] ), to much more sophisticated numerical methods developed in computational geom

This paper deals with the issue of the representation of space and motion, and argues that motion can be taken as a primitive notion on which a theory of space can be built, in which every object is an occurrent and has temporal parts. There has been a lot of discussion around the continuants/ occurrents opposition; while some authors have advocated the use of occurrents only for theories of parts and the geometry of common-sense, the few detailed or convincing work that has been devoted to solving the inherent problems of such an approach has made it easy for its detractors to claim it is a dead-end street. We present here a theory of spatio-temporal entities and show how this theory can be used to define a theory of motion. Thus we define a notion of continuity that is more appropriate than mathematical continuity for characterizing motion, and argue that we have here a basis for a theory of spatio-temporal objects.

We present here a theory of motion from a topological point of view, in a symbolic perspective. Taking space-time histories of objects as primitive entities, we introduce temporal and topological relations on the thus defined space-time to characterize classes of spatial changes. The theory thus accounts for qualitative spatial information, dealing with underspecified, symbolic information when accurate data is not available or unnecessary. We show that these structures give a basis for commonsense spatio-temporal reasoning by presenting a number of significant deductions in the theory. This can serve as a formal basis for languages describing motion events in a qualitative way.

In this paper, we present a spatial logic which can be used to reason about topological and spatial relationships among objects in spatial databases. The main advantages of such a formalism are its rigorousness, clear semantics and sound inference mechanism. We also show how the formalism can be extended to include orientation and metrical information. Comparisons with other formalisms are discussed.