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Qualitative Spatial Representation and Reasoning
 An Overview”, Fundamenta Informaticae
, 2001
"... 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 ..."
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Cited by 71 (10 self)
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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
Topology, connectedness, and modal logic
 ADVANCES IN MODAL LOGIC
, 2008
"... This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of ..."
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Cited by 5 (3 self)
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This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (lowdimensional) Euclidean spaces.
Regionbased Theories of Space: Mereotopology and Beyond (PhD Qualifying Exam Report, 2009)
"... The very nature of topology and its close relation to how humans perceive space and time make mereotopology an indispensable part of any comprehensive framework for qualitative spatial and temporal reasoning (QSTR). Within QSTR, it has by far the longest history, dating back to descriptions of pheno ..."
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Cited by 5 (2 self)
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The very nature of topology and its close relation to how humans perceive space and time make mereotopology an indispensable part of any comprehensive framework for qualitative spatial and temporal reasoning (QSTR). Within QSTR, it has by far the longest history, dating back to descriptions of phenomenological processes in nature (Husserl, 1913; Whitehead, 1920, 1929) – what we call today ‘commonsensical ’ in Artificial Intelligence. There have been plenty of other motivations to
Compactness and its implications for qualitative spatial and temporal reasoning
 PROCEEDINGS OF THE 13TH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR
, 2012
"... A constraint satisfaction problem has compactness if any infinite set of constraints is satisfiable whenever all its finite subsets are satisfiable. We prove a sufficient condition for compactness, which holds for a range of problems including those based on the wellknown Interval Algebra (IA) and ..."
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Cited by 4 (1 self)
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A constraint satisfaction problem has compactness if any infinite set of constraints is satisfiable whenever all its finite subsets are satisfiable. We prove a sufficient condition for compactness, which holds for a range of problems including those based on the wellknown Interval Algebra (IA) and RCC8. Furthermore, we show that compactness leads to a useful necessary and sufficient condition for the recently introduced patchwork property, namely that patchwork holds exactly when every satisfiable finite network (i.e., set of constraints) has a canonical solution, that is, a solution that can be extended to a solution for any satisfiable finite extension of the network. Applying these general theorems to qualitative reasoning, we obtain important new results as well as significant strengthenings of previous results regarding IA, RCC8, and their fragments and extensions. In particular, we show that all the maximal tractable fragments of IA and RCC8 (containing the base relations) have patchwork and canonical solutions as long as networks are algebraically closed.
Dynamic Mereotopology II: Axiomatizing some Whiteheadean Type Spacetime Logics
"... In this paper we present an Whiteheadean style pointfree theory of space and time. Here ”pointfree ” means that neither space points, nor time moments are assumed as primitives. The algebraic formulation of the theory, called dynamic contact algebra (DCA), is a Boolean algebra whose elements symbo ..."
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In this paper we present an Whiteheadean style pointfree theory of space and time. Here ”pointfree ” means that neither space points, nor time moments are assumed as primitives. The algebraic formulation of the theory, called dynamic contact algebra (DCA), is a Boolean algebra whose elements symbolize dynamic regions changing in time. It has three spatiotemporal relations between dynamic regions: space contact, time contact and preceding. We prove a representation theorem for DCAs of topological type, reflecting the dynamic nature of regions, which is a reason to call DCAs dynamic mereotopoly. We also present several complete quantifierfree logics based on the language of DCAs.
British Cataloguing in Publication Data
"... 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 ..."
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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 CataloginginPublication Data Qualitative spatiotemporal 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 applicationcentric research and providing a comprehensive perspective on the emerging area of qualitative spatiotemporal representation and reasoning” Provided by publisher.
Qualitative Spatial Representation and Reasoning
"... 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 fie ..."
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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
A NOTE ON THE THEORY OF COMPLETE MEREOTOPOLOGIES
"... Abstract. We investigate theories of Boolean algebras of regular sets of topological spaces. By RC(X), we denote the complete Boolean algebra of regular closed sets over a topological space X. By a mereotopology M over a topological space X, we denote every dense Boolean subalgebra of RC(X); M is c ..."
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Abstract. We investigate theories of Boolean algebras of regular sets of topological spaces. By RC(X), we denote the complete Boolean algebra of regular closed sets over a topological space X. By a mereotopology M over a topological space X, we denote every dense Boolean subalgebra of RC(X); M is called a complete mereotopology if it is a complete Boolean algebra. In this paper we consider mereotopologies as Lstructures, where L is the language of Boolean algebras extended with the binary relational symbol C interpreted as the contact relation. We show that the L−theories of complete mereotopologies and all mereotopologies are different. We also show that no complete mereotopology M, over a connected, compact, Hausdorff topological space X, is elementarily equivalent to a mereotopology M ′ , over X, that is a closed base for X and is finitely decomposable — i.e. every region in M ′ has only finitely many connected components. 1.