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B: “SNAP and SPAN: towards dynamic spatial ontology
 Spat Cogn Comput
"... We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic ..."
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Cited by 112 (12 self)
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We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic spatial ontology must combine these two distinct types of inventory of the entities and relationships in reality, and we provide characterizations of spatiotemporal reasoning in the light of the interconnections between them.
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 67 (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
D.C.: From video to RCC8: exploiting a distance based semantics to stabilise the interpretation of mereotopological relations
 Proc. COSIT, In Press (2011
"... Abstract. Mereotopologies have traditionally been defined in terms of the intersection of point sets representing the regions in question. Whilst these semantic schemes work well for purely topological aspects, they do not give any semantic insight into the degree to which the different mereotopolog ..."
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Cited by 14 (4 self)
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Abstract. Mereotopologies have traditionally been defined in terms of the intersection of point sets representing the regions in question. Whilst these semantic schemes work well for purely topological aspects, they do not give any semantic insight into the degree to which the different mereotopological relations hold. This paper explores this idea of a distance based interpretation for mereotopology. By introducing a distance measure between x and y, and for various Boolean combinations of x and y, we show that all the RCC8 relations can be distinguished. We then introduce a distance measure which combines these individual measures which we show reflect different paths through the RCC8 conceptual neighbourhood – i.e. the measure decreases/increases monotonically given certain monotonic transitions (such as one region expanding). There are several possible applications of this revised semantics; in the second half of the paper we explore one of these in some depth – the problem of abstracting mereotopological relations from noisy video data, such that the sequences of qualitative relations between pairs of objects do not suffer from “jitter”. We show how a Hidden Markov Model can exploit this distance based semantics to yield improved interpretation of video data at a qualitative level. 1
Stonian portholattices: A new approach to the mereotopology RT0
 ARTIFICIAL INTELLIGENCE
, 2009
"... This paper gives an isomorphic representation of the subtheories RT − , RT − EC, and RT of Asher and Vieu’s firstorder ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of portholattices – lattices that are bo ..."
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Cited by 7 (6 self)
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This paper gives an isomorphic representation of the subtheories RT − , RT − EC, and RT of Asher and Vieu’s firstorder ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of portholattices – lattices that are both orthocomplemented and pseudocomplemented – and show that the identity (x·y) ∗ = x ∗ +y ∗ defines the natural class of Stonian portholattices. Equivalent conditions for a portholattice to be Stonian are given. The main contribution of the paper consists of a representation theorem for RT − as Stonian portholattices. Moreover, it is shown that the class of models of RT − EC is isomorphic to the nondistributive Stonian portholattices and a representation of RT is given by a set of four algebras of which one need to be a subalgebra of the present model. As corollary we obtain that Axiom (A11) – existence of two externally connected regions – is in fact a theorem of the remaining axioms of RT.
Full mereogeometries
 Journal of Philosophical Logic
, 2007
"... Abstract. We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to iso ..."
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Cited by 6 (0 self)
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Abstract. We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of an environment structure is composed of particular subsets of Rn. The comparison of mereogeometrical theories within these environment structures shows dependencies among primitives and provides (relative) definitional equivalences. With one exception, we show that all the theories considered are equivalent in these environment structures. 1. Introduction. At the time Lobachevskii (1835
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
Semantic Interoperability of Geospatial Ontologies: A Model theoretic Analysis
, 2007
"... People sometimes misunderstand each other, even when they use the same language to communicate. Often these misunderstandings happen when people use the same words to mean different things, in effect disagreeing about meanings. This thesis investigates such disagreements about meaning, considering t ..."
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Cited by 2 (0 self)
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People sometimes misunderstand each other, even when they use the same language to communicate. Often these misunderstandings happen when people use the same words to mean different things, in effect disagreeing about meanings. This thesis investigates such disagreements about meaning, considering them to be issues of semantic interoperability. This thesis explores semantic interoperability via a particular formal framework used to specify people’s conceptualizations of a given domain. This framework is called an ‘ontology,’ which is a collection of data and axioms written in a logical language equipped with a modeltheoretic semantics. The domain under consideration is the geospatial domain. Specifically, this thesis investigates to what extent two geospatial ontologies are semantically interoperable when they ‘agree ’ on the meanings of certain basic terms and statements, but ‘disagree ’ on others. This thesis defines five levels of semantic interoperability that can exist between two ontologies. Each of these levels is, in turn, defined in terms of six ‘compatibility conditions, ’ which precisely describe how the results of queries to one ontology are compatible with the results of queries to another ontology. Using certain assumptions of finiteness, the semantics of each ontology is captured by a
Swiss Canton Regions: A Model for Complex Objects in Geographic Partitions
"... Abstract. Spatial regions are a fundamental abstraction of geographic phenomena. While simple regions—disklike and simply connected—prevail, in partitions complex configurations with holes and/or separations occur often as well. Swiss cantons are one highlighting example of these, bringing in addit ..."
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Abstract. Spatial regions are a fundamental abstraction of geographic phenomena. While simple regions—disklike and simply connected—prevail, in partitions complex configurations with holes and/or separations occur often as well. Swiss cantons are one highlighting example of these, bringing in addition variations of holes and separations with point contacts. This paper develops a formalism to construct topologically distinct configurations based on simple regions. Using an extension to the compound object model, this paper contributes a method for explicitly constructing a complex region, called a canton region, and also provides a mechanism to determine the corresponding complement of such a region.
RCC*9 and CBM*
"... Abstract. In this paper we introduce a new logical calculus of the Region Connection Calculus (RCC) family, RCC*9. Based on nine topological relations, RCC*9 is an extension of RCC8 and models topological relations between multitype geometric features: therefore, it is a calculus that goes beyo ..."
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Abstract. In this paper we introduce a new logical calculus of the Region Connection Calculus (RCC) family, RCC*9. Based on nine topological relations, RCC*9 is an extension of RCC8 and models topological relations between multitype geometric features: therefore, it is a calculus that goes beyond the modeling of regions as in RCC8, being able to deal with lower dimensional features embedded in a given space, such as linear features embedded in the plane. Secondly, the paper presents a modified version of the CalculusBased Method (CBM), a calculus for representing topological relations between spatial features. This modified version, called CBM*, is useful for defining a reasoning system, which was difficult to define for the original CBM. The two new calculi RCC*9 and CBM * are introduced together because we can show that, even if with different formalisms, they can model the same topological configurations between spatial features and the same reasoning strategies can be applied to them. 1