The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science

Qualitative reasoning about commonsense space often involves entities of different dimensions. We present a weak axiomatization of multidimensional qualitative space based on ‘relative dimension ’ and dimension-independent ‘containment ’ which suffice to define basic dimension-dependent mereotopological relations. We show the relationships to other meoreotopologies and to incidence geometry. The extension with betweenness, a primitive of relative position, results in a first-order theory that qualitatively abstracts ordered incidence geometry. 1

Reasoning about spatial knowledge is an important aspect of computational intelligence. Humans easily switch between high-level and low-level spatial knowledge, while computers have traditionally relied only on low-level spatial information. Qualitative spatial representation and reasoning is concerned with devising high-level, qualitative, representations of certain aspects of space using small sets of intuitive spatial relations that lend themselves to efficient reasoning. Many such representations have been developed over the years, but their use in practical applications seems to be inhibited. One reason preventing more widespread adoption of qualitative spatial representations may be the gap between simple but inexpressive qualitative representations at one end and geometric or quantitative representations with the expressivity of Euclidean geometry at the other end. Another factor may be the lack of semantic integration between the various spatial representations ranging from qualitative to geometric ontologies. We will address both issues in this thesis with a focus on spatial ontologies that involve some kind of mereotopological relations such as contact and parthood. We design a family of spatial ontologies with varying restrictiveness and increasingly more expressive nonlogical languages, organized into hierarchies of ontologies of equal expressivity. As the most founda-tional spatial ontology we propose a multidimensional mereotopology based only on ‘containment’ and

any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Qualitative spatio-temporal representation and reasoning: trends and future directions / Shyamanta M. Hazarika, editor. p. cm. Includes bibliographical references and index. Summary: “This book is a contribution to the emerging discipline of qualitative spatial information theory within artificial intelligence, covering both theory and application-centric research and providing a comprehensive perspective on the emerging area of qualitative spatio-temporal representation and reasoning”-- Provided by publisher.

Abstract. Many types of part-whole relations have been proposed in the literature to aid the conceptual modeller to choose the most appropriate type, but many of those relations lack a formal specification to give clear and unambiguous semantics to them. To remedy this, a formal taxonomy of types of mereological and meronymic part-whole relations is presented that distinguishes between transitive and intransitive relations and the kind of entity types that are related. The demand to use it effectively brings afore new requirements for automated reasoning over a hierarchy of relations. To ensure logically and ontologically correct inferencing over both the class and role hierarchy, the new reasoning service RBox compatibility for Description Logics reasoners is introduced. The proposed combination of formal semantics and the new reasoning service will improve the representation of

Qualitative reasoning about commonsense space often involves entities of different dimensions. We present a weak axiomatization of multidimensional qualitative space based on ‘relative dimension ’ and dimension-independent ‘containment ’ which suffice to define basic dimension-dependent mereotopological relations. We show the relationships to other meoreotopologies and to incidence geometry. The extension with betweenness, a primitive of relative position, results in a first-order theory that qualitatively abstracts ordered incidence geometry. 1