The paper proposes an approach to representing and reasoning about spatial regions with undetermined boundaries, using 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 approach proposed is referred to as thèegg-yolk' representation: a region with undetermined boundaries (a `vague region') is represented by a pair of concentric regions with deter-minate boundaries (`crisp regions'), which provide limits (not necessarily the tightest limits possible) on the range of indeterminacy.

This review discusses agent-based social simulation (ABSS) in relation tothe study of social dilemmas such as the Prisoner'sDilemma and Tragedy of the Commons . Its aims are to explore theplace of ABSS in relation to other research methods such asmathematical analysis, to familiariseartificial intelligence researchers (particularly those working onmulti-agent systems)with a body of relevant multidisciplinary work, and to suggest directionsfor future ABSS research on social dilemmas. ABSS research can contribute greatly to the understanding of socialphenomena, but needs to be based on a clear appreciation of the current`state of play' in the areas where it is used. With regard to `thin'(simple, general) simulation models, this primarily means attending towhat has been or could be discovered by mathematical analysis, to workusing other forms of simulation, and to the relevanttheoretical disputes; with regard to `thick' (specific, detailed) models(about which the paper has less to say), linking to the relevant`thin' models and to the empirical evidence. The bulk of ABSS work onsocial dilemmas has been concentratedin quite a narrow – though certainly significant – area (reciprocalaltruism in the Prisoner's Dilemma), and has sometimesbeen seriously flawed by over-ambitious claims, and insufficientattention to analytical approaches – although this same work has beenvery fertile in terms of inspiring further work, both analytical andsimulation-based.

This research report concerns the topology of 2-dimensional regions embedded in spherical surfaces, such as that of the Earth (`spherical regions'). It shows that the RCC (RegionConnection Calculus) rst-order logic formalism for qualitative spatial representation and reasoning is su ciently expressive to support a rich topological taxonomy of uniformly twodimensional regions forming parts of a spherical surface such as the Earth's. However, there are potentially useful constraints on the topology of such regions which the language of RCC cannot capture. Furthermore, the spherical model of the RCC axiom set developed here permits the construction of a proof that the theory axiomatised by this axiom set is undecidable (a result also derivable from (Grzegorczyk 1951).

This paper describes some well-defined types of emergence that occur in a class of large, initially random arrays of a well-known binary cellular automaton, Conway's 'Game of Life'. Results concerning the existence or non-existence of finite patterns with particular properties are used to advance the global analysis. It is shown that in infinite (and very large finite) arrays of the Game of Life with initially sparse and randomly distributed non-uniformities, self-organized construction processes will lead to the emergence of coherent structures which have crucial effects on the medium-term dynamics of the array. Directions for future research are suggested.

Abstract Artificial Intelligence (Al) must secure rigorously derived formal theories that support our everyday understanding of properties of space and time if intelligent autonomous machines are eventually to be produced. Without such a foundation, we have no means to verify whether any program will function correctly, or indeed, safely. Over the last decade temporal logics have been extensively and successfully used as formal tools in both AI and software engineering-see for example, Galton (1987). Logics describing space have not been developed and exploited to the same degree, although there has been more interest recently. Our research assumes that it is desirable to do this in order to place future applications of spatial reasoning on a sound foundation. Spatial logics also have uses in software engineering-in the visualization and animation of pro grams (Kahn and Saraswat, 1990).

It is argued that rigorous formal theories are a necessity if proper use is to be made ofcomputers" ability to store and manipulate spatial and spatiotemporal information. A qualitativespatial calculus constructed within first-order logic is described. This calculus treats extendedregions rather than points as fundamental, and is based on primitive concepts of `connection'between regions, and of convexity. A sorted logic, and subsumption lattices of spatial relationsand of spatial and ...

The paper reports work on the topological formalism `RCC', a region-based `calculus of connection' developed at Leeds university over the past several years. Speci cally, it is shown that the nonempty regular closed sets of a class of topological spaces (connected T3-spaces) provide models for the RCC axiom-set. A brief assessment is made of RCC's potential as a formalism for applications in the area of spatial information systems (SIS). Two approaches to developing topological formalisms for SIS are compared, and a parallel is drawn with the two main parts of topology as understood by mathematicians.

Topological formalisms adaptable to a wide range of applications in spatial information systems (SIS) are a highly desirable research goal. The paper discusses a candidate formalism, the region-based `logic of connection' of Randell, Cohn and Cui. This is based on the single primitive `C' (where `C(x; y)' indicates that spatial regions x and y are `connected'). The originators of this approach (`RCC theory') de ned a set of eight `base relations', exactly one of which holds between any pair of regions. It is shown how ner distinctions between topological relations than those provided by these base relations, and taxonomies of topological properties of regions, can be de ned using RCC theory. Both the surprising expressiveness of RCC, and some of its drawbacks, are illustrated using an example problem: how to determine whether a region has the topology of a `doughnut' (solid torus) by asking questions using only terms derived from C. It is shown how the task could be performed given certain assumptions about the target region and about regions in general. These are then progressively relaxed; as this is done, the task requires the de nition of further terminology, all derived ultimately from `C', providing a basis for successively broader and ner taxonomies of topological properties and relationships, but also revealing features of spatial relations which are di cult to capture within RCC.

L'A. developpe une approche de la formalisation de la description et du raisonnement topologiques (theorie RCC, calcul de connexion des regions) qui offre une alternative au modele mathematique conventionnel. Fondee sur des entites spatiales plutot que sur des classes d'espaces, cette approche permet d'etablir des liens entre les concepts fondamentaux de la topologie

Spatial reasoning is crucial in many AI application domains, such as robotics, qualitative and naive physics, and some types of planning. Qualitative reasoning is often required ; and in many of these cases, uncertainty or imprecision about the spatial extent of particular entities has to be represented and coped with. This paper develops an axiomatisation of a relation of`crisping' (reducing imprecision or vagueness) between pairs of`vague' spatial regions: those with indeterminate boundaries. This axiomatisa-tion is then related to the previously devel-opedègg-yolk' representation of vagueness, originally designed by (Lehmann and Cohn 1994) for database applications, then applied to expressing spatial vagueness by (Cohn and Gotts 1996). We gratefully acknowledge the support of the EPSRC under grant GR/H/78955 and also the CEC under the Basic Research Action MEDLAR 2, Project 6471. We also acknowledge useful discussions with the rest of the QSR group at Leeds and Eliseo Clementini.

The need for a formal language in which to express and reason about spatial concepts is of crucial importance in many areas of AI and visual systems. For the last five years, spatial reasoning research by the Qualitative Spatial Reasoning Group, University of Leeds, has centred on the development and application of such a language — the RCC spatial logic. Below, we briefly describe the work of the group in this area.

Qualitative descriptions of spatial properties and relationships, and qualitativespatial reasoning, are of fundamental importance in human problemsolving:even where we use quantitative approaches, these depend on an accompanyingqualitative representation. The work described is aimed at formalisingsome topological aspects of qualitative spatial description and reasoning.The paper continues the work of Randell, Cohn and Cui on region-basedqualitative representations of spatial...

The paper proposes considers the problem of representing and reasoningabout spatial regions with undetermined boundaries. First we build a firstorder theory of such regions and then propose a possible translation this theoryinto an adaptation of `RCC-theory", a region-based system for representingqualitative spatial relations developed over the last few years (Randell, Cuiand Cohn 1992, Cohn, Randell and Cui 1994). The proposed translationis referred to as the `egg-yolk"...

It is argued that rigorous formal theories are a necessity if proper use is to be made of computers' ability to store and manipulate spatial and spatiotemporal information. A qualitative spatial calculus constructed within rst-order logic is described. This calculus treats extended regions rather than points as fundamental, and is based on primitive concepts of`connection' between regions, and of convexity. A sorted logic, and subsumption lattices of spatial relations and of spatial and temporal entities, are used to implement the calculus. Inference mechanisms used to reason about both static and dynamic sets of relations between regions are described, and the notion of`conceptual neighbourhoods' within sets of relations is explored. We discuss an example drawn from the domain of biology, and suggest possible applications within geography and related areas. The paper concludes with a description of current and projected work based on our qualitative spatial calculus.

The paper considers the problem of representing and reasoning about spatial regions with undetermined boundaries. We start by building a rst order theory of such regions; then we propose a possible translation from 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 thèegg-yolk' representation: a region with undetermined boundaries (a `vague region') is represented by a pair of concentric regions with determinate boundaries (`crisp re-gions'), which provide limits (not necessarily the tightest limits possible) on the range of indeterminacy.