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450
Qualitative Spatial Reasoning: Cardinal Directions as an Example
, 1996
"... Geographers use spatial reasoning extensively in largescale spaces, i.e., spaces that cannot be seen or understood from a single point of view. Spatial reasoning differentiates several spatial relations, e.g. topological or metric relations, and is typically formalized using a Cartesian coordinate ..."
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Cited by 99 (7 self)
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Geographers use spatial reasoning extensively in largescale spaces, i.e., spaces that cannot be seen or understood from a single point of view. Spatial reasoning differentiates several spatial relations, e.g. topological or metric relations, and is typically formalized using a Cartesian coordinate system and vector algebra. This quantitative processing of information is clearly different from the ways humans draw conclusions about spatial relations. Formalized qualitative reasoning processes are shown to be a necessary part of Spatial Expert Systems and Geographic Information Systems. Addressing a subset of the total problem, namely reasoning with cardinal directions, a completely qualitative method, without recourse to analytical procedures, is introduced and a method for its formal comparison with quantitative formulae is defined. The focus is on the analysis of cardinal directions and their properties. An algebraic method is used to formalize the meaning of directions. The standard...
Spatial Reasoning with Propositional Logics
 Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR94
, 1994
"... I present a method for reasoning about spatial relationships on the basis of entailments in propositional logic. Formalisms for representing topological and other spatial information (e.g. [2] [10] [11]) have generally employed the 1storder predicate calculus. Whilst this language is much more expr ..."
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Cited by 98 (15 self)
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I present a method for reasoning about spatial relationships on the basis of entailments in propositional logic. Formalisms for representing topological and other spatial information (e.g. [2] [10] [11]) have generally employed the 1storder predicate calculus. Whilst this language is much more expressive than 0order (propositional) calculi it is correspondingly harder to reason with. Hence, by encoding spatial relationships in a propositional representation automated reasoning becomes more effective. I specify representations in both classical and intuitionistic propositional logic, which  together with welldefined metalevel reasoning algorithms  provide for efficient reasoning about a large class of spatial relations. 1 INTRODUCTION This work has developed out of research done by Randell, Cui and Cohn (henceforth RCC) on formalising spatial and temporal concepts used in describing physical situations [11]. A set of classical 1storder logic axioms has been formulated in whi...
Econnections of abstract description systems
"... Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is chal ..."
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Cited by 95 (25 self)
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Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows nontrivial interactions between the combined components. The new method, called Econnection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of Econnections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of nary ‘link relations. ’ We define several natural variants of Econnections and study indepth the transfer of decidability from the component systems to their Econnections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.
Qualitative Representation of Positional Information
 ARTIFICIAL INTELLIGENCE
, 1997
"... A framework for the qualitative representation of positional information in a twodimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flex ..."
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Cited by 91 (3 self)
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A framework for the qualitative representation of positional information in a twodimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning. Knowledge about position in largescale space is commonly represented by a combination of orientation and distance relations, which we express in a particular frame of reference between a primary object and a reference object. While the representation of orientation comes out to be more straightforward, the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared; this is done by defining structure relations that are able to handle, among others, order of magnitude relations; the frame of reference with its three components (distance system, s...
Mereotopology: a theory of parts and boundaries
 Data & Knowledge Engineering
, 1996
"... The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes. to relations of contact and connectedness. to the concepts of surface, point, neighbourhood. and so on. The basis of the theory ..."
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Cited by 88 (19 self)
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The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes. to relations of contact and connectedness. to the concepts of surface, point, neighbourhood. and so on. The basis of the theory is mereology. the formal theory of part and whole, a theory which is shown to have a number of advantages. for ontological purposes. over standard treatments of topology in settheoretic terms. One central goal of the paper is to provide a rigorous formulation of B~ntano's thesis to the effect that a boundary can exist as a matter of necessity only as part of a whole of higher dimension of which it is the boundary. It concludes with a brief survey of current applications of mereotopology in areas such as naturallanguage analysis, geographic information systems, machine vision, naive physics, and database and knowledge engineering.
Modal Logics for Qualitative Spatial Reasoning
, 1996
"... Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate highlevel qualitative spatial information ..."
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Cited by 82 (12 self)
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Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate highlevel qualitative spatial information in a flexible way would be extremely useful. Such capabilities can be proveded by logical calculi; and indeed 1storder theories of certain spatial relations have been given [20]. But computing inferences in 1storder logic is generally intractable unless special (domain dependent) methods are known. 0order modal logics provide an alternative representation which is more expressive than classical 0order logic and yet often more amenable to automated deduction than 1storder formalisms. These calculi are usually interpreted as propositional logics: nonlogical constants are taken as denoting propositions. However, they can also be given a nominal interpretation in which the constants stand...
A Pointless Theory of Space Based on Strong Connection and Congruence
 In Proceedings of Principles of Knowledge Representation and Reasoning (KR96
, 1996
"... We present a logical theory of space where only tridimensional regions are assumed in the domain. Three distinct primitives are used to describe their mereological, topological and morphological properties: mereology is described by a parthood relation satisfying the axioms of Closed Extensional Mer ..."
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Cited by 82 (11 self)
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We present a logical theory of space where only tridimensional regions are assumed in the domain. Three distinct primitives are used to describe their mereological, topological and morphological properties: mereology is described by a parthood relation satisfying the axioms of Closed Extensional Mereology; topology is described by means of a "simple region" predicate, by which a relation of “strong connection ” between regions having at least a surface in common is defined; morphology is described by means of a "congruence " primitive, whose axioms exploit Tarski's analogy between points and spheres. 1
Qualitative Representation of Spatial Knowledge in TwoDimensional Space
, 1994
"... Various relationbased systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the represen ..."
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Cited by 71 (22 self)
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Various relationbased systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems, and we outline the computational tasks involved in relationbased spatial information processing. We also describe symbolic spatial indexes, relationbased structures that combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modeling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed to define the relations of the modeling space. By keeping the relative arrangements of the representative points in symbolic spatial indexes and discarding all other points, we maintain enough information to answer queries regarding the spatial relations of the modeling space without the need to access the initial image or an object database. Symbolic spatial indexes can be used to solve problems involving route planning, composition of spatial relations, and update operations.
Semiotic Schemas: A Framework for Grounding Language in Action and Perception
, 2005
"... A theoretical framework for grounding language is introduced that provides a computational path from sensing and motor action to words and speech acts. The approach combines concepts from semiotics and schema theory to develop a holistic approach to linguistic meaning. Schemas serve as structured be ..."
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Cited by 69 (10 self)
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A theoretical framework for grounding language is introduced that provides a computational path from sensing and motor action to words and speech acts. The approach combines concepts from semiotics and schema theory to develop a holistic approach to linguistic meaning. Schemas serve as structured beliefs that are grounded in an agent’s physical environment through a causalpredictive cycle of action and perception. Words and basic speech acts are interpreted in terms of grounded schemas. The framework reflects lessons learned from implementations of several language processing robots. It provides a basis for the analysis and design of situated, multimodal communication systems that straddle symbolic and nonsymbolic realms.
Topological Relations Between Regions With Holes
 Int. Journal of Geographical Information Systems
, 1994
"... The 4intersection, a model for the representation of topological relations between 2dimensional objects with connected boundaries and connected interiors, is extended to cover topological relations between 2dimensional objects with arbitrary holes, called regions with holes. Each region with hole ..."
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Cited by 68 (3 self)
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The 4intersection, a model for the representation of topological relations between 2dimensional objects with connected boundaries and connected interiors, is extended to cover topological relations between 2dimensional objects with arbitrary holes, called regions with holes. Each region with holes is represented by its generalized regionthe union of the object and its holes and the closure of each hole. The topological relation between two regions with holes, A and B, is described by the set of all individual topological relations between (1) A 's generalized region and B's generalized region, (2) A 's generalized region and each of B's holes, (3) B's generalized region with each of A 's holes, and (4) each of A 's holes with each of B's holes. As a side product, the same formalism applies to the description of topological relations between 1spheres. An algorithm is developed that minimizes the number of individual topological relations necessary to describe a configuration completely. This model of representing complex topological relations is suitable for a multilevel treatment of topological relations, at the least detailed level of which the relation between the generalized regions prevails. It is shown how this model applies to the assessment of consistency in multiple representations when, at a coarser level of less detail, regions are generalized by dropping holes.