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A Spatial Logic based on Regions and Connection
 PROCEEDINGS 3RD INTERNATIONAL CONFERENCE ON KNOWLEDGE REPRESENTATION AND REASONING
, 1992
"... We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its us ..."
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Cited by 565 (29 self)
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We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its useful expressiveness. An axiomatisation of the new theory and a comparison with the two original theories is given.
Qualitative Spatial Representation and Reasoning: An Overview
 FUNDAMENTA INFORMATICAE
, 2001
"... The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning inclu ..."
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Cited by 179 (16 self)
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The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33, 34].
L.: Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology
 in: IJCAI95
"... Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the semantics of natural language expressions concerning locations and relative positions. While several authors have proposed axioms for these notions, no one with the exception ..."
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Cited by 103 (0 self)
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Mereological and topological notions of connection, part, interior and complement are central to spatial reasoning and to the semantics of natural language expressions concerning locations and relative positions. While several authors have proposed axioms for these notions, no one with the exception of Tarski [18], who based his axiomatization of mereological notions on a Euclidean metric, has attempted to give them a semantics. We offer an alternative to Tarski, starting with mereotopological notions that have proved useful in the semantic analysis of spatial expressions. We also give a complete axiomatization of this account of mereotopological reasoning. 1
Parts, Wholes, and PartWhole Relations: The Prospects of Mereotopology
 Data and Knowledge Engineering
, 1996
"... INTRODUCTION This is a brief overview of formal theories concerned with the study of the notions of (and the relations between) parts and wholes. The guiding idea is that we can distinguish between a theory of parthood (mereology) and a theory of wholeness (holology, which is essentially afforded b ..."
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Cited by 62 (13 self)
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INTRODUCTION This is a brief overview of formal theories concerned with the study of the notions of (and the relations between) parts and wholes. The guiding idea is that we can distinguish between a theory of parthood (mereology) and a theory of wholeness (holology, which is essentially afforded by topology), and the main question examined is how these two theories can be combined to obtain a unified theory of parts and wholes. We examine various nonequivalent ways of pursuing this task, mainly with reference to its relevance to spatiotemporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) theories; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory subsuming mereology. This is done in Sections 4 through 6. We also consider some more speculative strategies and directions for further research. First, however, we begin with some preliminary outline of
A Qualitative Theory of Motion Based on SpatioTemporal Primitives
, 1998
"... This paper presents a formal theory for reasoning about motion of spatial entities, in a qualitative framework. Taking over a theory intended for spatial entities, we enrich it to achieve a theory whose intended models are spatiotemporal entities, an idea sometimes proposed by philosophers or ..."
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Cited by 55 (1 self)
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This paper presents a formal theory for reasoning about motion of spatial entities, in a qualitative framework. Taking over a theory intended for spatial entities, we enrich it to achieve a theory whose intended models are spatiotemporal entities, an idea sometimes proposed by philosophers or AI authors but never fully exploited. We show what kind of properties usually assumed as desirable parts of any spacetime theory are recovered from our model, thus giving a sound theoretical basis for a natural, qualitative representation of motion.
Taxonomies of Logically Defined Qualitative Spatial Relations
 IN N. GUARINO AND R. POLI (EDS), FORMAL ONTOLOGY IN CONCEPTUAL ANALYSIS AND KNOWLEDGE REPRESENTATION
, 1994
"... This paper develops a taxonomy of qualitative spatial relations for pairs of regions, which are all logically defined from two primitive (but axiomatised) notions. The first primitive is the notion of two regions being connected, which allows eight jointly exhaustive and pairwise disjoint relations ..."
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Cited by 48 (21 self)
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This paper develops a taxonomy of qualitative spatial relations for pairs of regions, which are all logically defined from two primitive (but axiomatised) notions. The first primitive is the notion of two regions being connected, which allows eight jointly exhaustive and pairwise disjoint relations to be defined. The second primitive is the convex hull of a region which allows many more relations to be defined. We also consider the development of the useful notions of composition tables for the defined relations and networks specifying continuous transitions between pairs of regions. We conclude by discussing what kind of criteria to apply when deciding how fine a taxonomy to create.
Qualitative SpatioTemporal Representation and Reasoning: A Computational Perspective
 Exploring Artifitial Intelligence in the New Millenium
, 2001
"... this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science fict ..."
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Cited by 30 (11 self)
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this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science fiction writers, and were of vital concern to our everyday life and commonsense reasoning. So whatever approach to AI one takes [ Russell and Norvig, 1995 ] , temporal and spatial representation and reasoning will always be among its most important ingredients (cf. [ Hayes, 1985 ] ). Knowledge representation (KR) has been quite successful in dealing separately with both time and space. The spectrum of formalisms in use ranges from relatively simple temporal and spatial databases, in which data are indexed by temporal and/or spatial parameters (see e.g. [ Srefik, 1995; Worboys, 1995 ] ), to much more sophisticated numerical methods developed in computational geom
Topological SpatioTemporal Reasoning and Representation
, 2002
"... We present here a theory of motion from a topological point of view, in a symbolic perspective. Taking spacetime histories of objects as primitive entities, we introduce temporal and topological relations on the thus defined spacetime to characterize classes of spatial changes. The theory thus acc ..."
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Cited by 22 (1 self)
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We present here a theory of motion from a topological point of view, in a symbolic perspective. Taking spacetime histories of objects as primitive entities, we introduce temporal and topological relations on the thus defined spacetime to characterize classes of spatial changes. The theory thus accounts for qualitative spatial information, dealing with underspecified, symbolic information when accurate data is not available or unnecessary. We show that these structures give a basis for commonsense spatiotemporal reasoning by presenting a number of significant deductions in the theory. This can serve as a formal basis for languages describing motion events in a qualitative way.
SpaceTime as a Primitive for Space and Motion
, 1998
"... This paper deals with the issue of the representation of space and motion, and argues that motion can be taken as a primitive notion on which a theory of space can be built, in which every object is an occurrent and has temporal parts. There has been a lot of discussion around the continuants/ oc ..."
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Cited by 21 (1 self)
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This paper deals with the issue of the representation of space and motion, and argues that motion can be taken as a primitive notion on which a theory of space can be built, in which every object is an occurrent and has temporal parts. There has been a lot of discussion around the continuants/ occurrents opposition; while some authors have advocated the use of occurrents only for theories of parts and the geometry of commonsense, the few detailed or convincing work that has been devoted to solving the inherent problems of such an approach has made it easy for its detractors to claim it is a deadend street. We present here a theory of spatiotemporal entities and show how this theory can be used to define a theory of motion. Thus we define a notion of continuity that is more appropriate than mathematical continuity for characterizing motion, and argue that we have here a basis for a theory of spatiotemporal objects.
Reasoning About Space: The Hole Story
 Logic and Logical Philosophy
, 1996
"... this paper is to elaborate on that formalism and to illustrate how it can be exploited to provide a framework for more general patterns of REASONING ABOUT SPACE: THE HOLE STORY ..."
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Cited by 15 (11 self)
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this paper is to elaborate on that formalism and to illustrate how it can be exploited to provide a framework for more general patterns of REASONING ABOUT SPACE: THE HOLE STORY