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 proposes an approach to representing and reasoning about spatial regions with undetermined boundaries, using an adaptation of `RCC-theory', a regionbased system for representing qualitative spatial relations developed over the last few years (Randell, Cui and Cohn 1992, Cohn, Randell and Cui 1994). The approach proposed is referred to as the `egg-yolk' representation: a region with undetermined boundaries (a `vague region') is represented by a pair of concentric regions with determinate boundaries (`crisp regions'), which provide limits (not necessarily the tightest limits possible) on the range of indeterminacy. 1 Introduction The topic of this paper is how best to deal with vagueness in spatial representation and reasoning, particularly within the framework of `RCC-theory', (Randell, Cui and Cohn 1992, Cohn et al. 1994), which provides a representation of topological properties and relations in which regions rather than points are taken as primitive. We are concern...

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

We describe an envisionment-based qualitative simulation program. The program implements part of an axiomatic, first order theory that has been developed to represent and reason about space and time. Topological information from the modelled domain is expressed as sets of distinct topological relations holding between sets of objects. These form the qualitative states in the underlying theory and simulation. Processes in the theory are represented as paths in the envisionment tree. The algorithm is illustrated with an example of a simulation of phagocytosis and exocytosis - two processes used by unicellular organisms for garnering food and expelling waste material respectively. Introduction Envisionment-based simulation programs used in Qualitative Reasoning (QR) are now well established. The notion of an envisionment originated in de Kleer's NEWTON program, but now appears as a central program design feature in many QR simulation programs - see Weld and de Kleer (1990)...

. 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...

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.

this paper is to elaborate on that formalism and to illustrate how it can be exploited to provide a framework for more general patterns of REASONING ABOUT SPACE: THE HOLE STORY

. In this paper we review previous work on non modal spatial logics and explore a corresponding modal spatial logic. Furthermore we present an initial classification of kinds of spatially indexed propositions. 1 Introduction Although the use of interval temporal logics has been an active research area in AI for some time, the analogous development of ontologies for space and spatial logics based on regions has only relatively recently started to become a serious research activity (eg Pribbenow and Schlieder 1992, Narayan 1992). Various approaches have been promulgated; for example one can simply use Allen's (1983) temporal relations on each of the cartesian axes to specify the qualitative relationship between two regions (eg Hernandez 1990, Mukerjee and Joe 1990), but this has the disadvantage of either requiring knowledge about the absolute orientation of the two regions or their orientation relative to a fixed viewpoint. For many applications one might only have local information a...

this paper). Links are undirected curves that link two ports. Channels are directed curves linking two ports (an arrow is used to indicate directionality). Finally, a call arrow is a directed curve from within an agent contour to the contour of another agent.

The paper proposes considers the problem of representing and reasoning about spatial regions with undetermined boundaries. First we build a first order theory of such regions and then propose a possible translation this theory into an adaptation of `RCC-theory', a region-based system for representing qualitative spatial relations developed over the last few years (Randell, Cui and Cohn 1992, Cohn, Randell and Cui 1994). The proposed translation is referred to as the `egg-yolk' representation: a region with undetermined boundaries (a `vague region') is represented by a pair of concentric regions with determinate boundaries (`crisp regions'), which provide limits (not necessarily the tightest limits possible) on the range of indeterminacy. 1 Introduction The topic of this paper 1 is how best to deal with vagueness in spatial representation and reasoning, particularly within the framework of `RCC-theory', (Randell, Cui and Cohn 1992, Cohn et al. 1994), which provides a repres...