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Relation algebras and their application in temporal and spatial reasoning
 In: Artif. Intell. Rev
"... Abstract Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations ..."
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Abstract Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations must exist, given several basic operations, such as Boolean operations on relations, relational composition and converse. Each equation in the calculus corresponds to a theorem, and, for a situation where there are only nitely many relations, one can construct a composition table which can serve as a look up table for the relations involved. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. In this sense, relational calculus is pointless. Relation algebras were introduced into temporal reasoning by Allen [1] and into spatial reasoning by Egenhofer and Sharma
A Proof System for Contact Relation Algebras
"... Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa & Sikorski (1963) for relatio ..."
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Cited by 17 (12 self)
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Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa & Sikorski (1963) for relation algebras generated by a contact relation. 1 Introduction Contact relations arise in the context of qualitative geometry and spatial reasoning, going back to the work of de Laguna (1922), Nicod (1924), Whitehead (1929), and, more recently, of Clarke (1981), Cohn et al. (1997), Pratt & Schoop (1998, 1999) and others. They are a generalisation of the "overlap relation" , obtained from a "part of" relation, which for the first time was formalised by Lesniewski (1916), (see also Lesniewski, 1983). One of Lesniewski's main concerns was to build a paradoxfree foundation of Mathematics, one pillar of which was mereology 1 or, as it was originally called, the general theory of manifolds or colle...
Algebraization and representation of mereotopological structures
 JoRMiCS
, 2004
"... Abstract. Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems. 1 ..."
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Abstract. Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems. 1
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
Customizing Qualitative Spatial and Temporal Calculi
"... Abstract. Qualitative spatial and temporal calculi are usually formulated on a particular level of granularity and with a particular domain of spatial or temporal entities. If the granularity or the domain of an existing calculus doesn’t match the requirements of an application, it is either possibl ..."
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Abstract. Qualitative spatial and temporal calculi are usually formulated on a particular level of granularity and with a particular domain of spatial or temporal entities. If the granularity or the domain of an existing calculus doesn’t match the requirements of an application, it is either possible to express all information using the given calculus or to customize the calculus. In this paper we distinguish the possible ways of customizing a spatial and temporal calculus and analyze when and how computational properties can be inherited from the original calculus. We present different algorithms for customizing calculi and proof techniques for analyzing their computational properties. We demonstrate our algorithms and techniques on the Interval Algebra for which we obtain some interesting results and observations. We close our paper with results from an empirical analysis which shows that customizing a calculus can lead to a considerably better reasoning performance than using the noncustomized calculus. 1
A Reconciliation of Logical Representations of Space: from Multidimensional Mereotopology to Geometry
, 2013
"... Reasoning about spatial knowledge is an important aspect of computational intelligence. Humans easily switch between highlevel and lowlevel spatial knowledge, while computers have traditionally relied only on lowlevel spatial information. Qualitative spatial representation and reasoning is concer ..."
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Reasoning about spatial knowledge is an important aspect of computational intelligence. Humans easily switch between highlevel and lowlevel spatial knowledge, while computers have traditionally relied only on lowlevel spatial information. Qualitative spatial representation and reasoning is concerned with devising highlevel, 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 foundational spatial ontology we propose a multidimensional mereotopology based only on ‘containment’ and
Relation algebras and their application in qualitative spatial reasoning
, 2005
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The Complexity of Constraint Satisfaction Problems For Small Relation Algebras
"... Andreka and Maddux (1994, Notre Dame Journal of Formal Logic, 35(4)) classified the small relation algebras  those with at most 8 elements, or in other terms, at most 3 atomic relations. They showed that there are eighteen isomorphism types of small relation algebras, all representable. For each s ..."
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Andreka and Maddux (1994, Notre Dame Journal of Formal Logic, 35(4)) classified the small relation algebras  those with at most 8 elements, or in other terms, at most 3 atomic relations. They showed that there are eighteen isomorphism types of small relation algebras, all representable. For each simple, small relation algebra they computed the spectrum of the algebra, namely the set of cardinalities of square representations of that relation algebra.
Relational reasoning in the Region Connection Calculus ∗
, 2005
"... This paper is mainly concerned with the relationalgebraical aspects of the wellknown Region Connection Calculus (RCC). We show that the contact relation algebra (CRA) of certain RCC model is not atomic complete and hence infinite. So in general an extensional composition table for the RCC cannot b ..."
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This paper is mainly concerned with the relationalgebraical aspects of the wellknown Region Connection Calculus (RCC). We show that the contact relation algebra (CRA) of certain RCC model is not atomic complete and hence infinite. So in general an extensional composition table for the RCC cannot be obtained by simply refining the RCC8 relations. After having shown that each RCC model is a consistent model of the RCC11 CT, we give an exhaustive investigation about extensional interpretation of the RCC11 CT, where we attach a superscript × to a cell entry in the table if and only if extensional interpretation is impossible for this entry. More important, we show the complemented closed disk algebra is a representation for the relation algebra determined by the RCC11 table. The domain of this algebra contains two classes of regions, the closed disks and closures of their complements in the real plane, and the contact relation is standard Whiteheadean contact (i.e. aCb iff a ∩ b = ∅).
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.