We show that string graphs can be recognized in nondeterministic exponential time by giving an exponential upper bound on the number of intersections for a minimal drawing realizing a string graph in the plane. This upper bound confirms a conjecture by Kratochvl and Matousek [KM91] and settles the long-standing open problem of the decidability of string graph recognition (Sinden [Sin66], Graham [Gra76]). Finally we show how to apply the result to solve another old open problem: deciding the existence of Euler diagrams, a fundamental problem of topological inference (Grigni, Papadias, Papadimitriou [GPP95]). The general theory of Euler diagrams turns out to be as hard as second-order arithmetic.

This paper shows by a constructive method the existence of a diagrammatic representation called extended Euler diagrams for any collection of sets X1 , ..., Xn , n 9. These diagrams are adapted for representing sets inclusions and intersections: each set X i and each non empty intersection of a subcollection of X1 , ..., Xn is represented by a unique connected region of the plane. Starting with an abstract description of the diagram, we define the dual graph G and reason with the properties of this graph to build a planar representation of the X1 , ..., Xn . These diagrams will be used to visualize the results of a complex request on any indexed video databases. In fact, such a representation allows the user to perceive simultaneously the results of his query and the relevance of the database according to the query.

We propose to model some diagrammatic reasoning tasks with a topological framework. We are not interested in reasoning on diagrams but in reasoning on a problem with a diagrammatic representation. A diagrammatic representation is formalised with topological objects, and the reasoning processed on it is modeled with topological operations. We present here three applications to illustrate the idea that combinatorial algebraic topology is an adequate and unifying framework to specify and analyse diagrammatic representations and diagrammatic reasoning. The first application presented is a categorisation problem, the second concerns hierarchy structuring, and the third is the ESQIMO system for solving analogies in unsupervised IQ-tests. Introduction Diagrammatic reasoning is a field of research investigating the use of spatial relations for knowledge processing. This includes knowledge representations, retrieval processing, inference making, etc. Several issues are addressed in these acti...

We present a novel approach to mapbuilding and target area identification in mobile robotics -- its emphasis being on the efficiency of multiple resolution representations for mapping and goal-area identification (for example, for the purpose of mobile robot self-localisation). After presenting and analysing the experimental results, we examine the scientific status of the research carried out, and of the field of mobile robotics in general. We argue that there is an implicit theory of mobile robotics, but that -- for the future health of the discipline -- it needs to be extended and made explicit through the development of an appropriate theoretical language and formal models. After exploring the relationship between design, engineering, and science, we argue that mobile robotics still lacks falsifiable theories of robot--environment interaction. This leads us to propose some desirable future directions for the discipline of mobile robotics as a maturing science. 1998 Elsevier Science...

Abstract—Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of well-formedness conditions; we present a series of results that identify properties of cycles that correspond to the well-formedness conditions. This improves upon other contributions toward the automated generation of Euler diagrams which implicitly assume some fixed set of well-formedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed.

In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposal of Englebretsen; we thus draw a more general moral about the use of spatial relations in representation systems. 1 Diagrammatic representation systems Diagrammatic represent...

l entities: they are are built of simpler constituents and/or together with other entities build more complex wholes. The word Places tells us that dealing with space is dealing with locations and located entities. The book brings mereotopology to a wider public, by using simple words next to more technical ones and by providing several examples from our everyday experience of space next to formal theories of space. Furthermore, it provides a vast survey of the field, ranging from the seminal work of Whitehead to the most recent publications, which makes it an excellent starting point for the graduate student and researcher interested in qualitative formal representations of space. The reader interested in implementing spatial related systems might consider the prevalent philosophical view of the field to be a werakness. She/he will sometimes get lost in the philosophical subtleties of the more abstract concepts and, at times, wonder about possible implications of the conclusions reach

Abstract. Conceptual Graphs are a common knowledge representation system which are used in conjunction with an explicit type hierarchy of the domain. However, this means the interpretation of information expressed in conceptual graphs requires the combined use of information from different sources, which is not always an easy cognitive task. Though it is possible to explicitly represent the type hierarchy with Conceptual Graphs with Cuts, this less natural expression of the type hierarchy information is not as easy to interpret and soon takes up a lot of space. Now, one of the main advantages of Euler diagram-based notations like Spider diagrams is the natural diagrammatic representation of hierarchies. However, Spider diagrams lack facilities such as the ability to represent general relationships between objects which is necessary for knowledge representation tasks. We bring together the most pertinent features of both of these notations, creating a new hybrid notation called Conceptual Spider Diagrams. We provide formal syntax and semantics of this new notation, together with examples demonstrating its capabilities. 1

Elements from the technical works

Abstract. Using the notion of planarity and drawing for hypergraphs introduced respectively by Johnson and Pollak [9] and Mäkinen [14], we show in this paper that any hypergraph having less than nine hyperedges is vertex-planar and can be drawn in the edge standard and in the subset standard without edge crossing. Key words: hypergraphs, planarity, vertex-planarity, drawing in the edge standard, drawing in the subset standard, Euler diagrams 1