Results 1  10
of
26
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 ..."
Abstract

Cited by 264 (18 self)
 Add to MetaCart
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].
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 ..."
Abstract

Cited by 71 (10 self)
 Add to MetaCart
(Show Context)
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
Boolean Connection Algebras: A New Approach to the RegionConnection Calculus
 Artificial Intelligence
, 1999
"... The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and prove ..."
Abstract

Cited by 50 (6 self)
 Add to MetaCart
(Show Context)
The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and proves that these structures are equivalent to models of the RCC axioms. BCAs permit a wealth of results from the theory of lattices and boolean algebras to be applied to RCC. This is demonstrated by two theorems which provide constructions for BCAs from suitable distributive lattices. It is already well known that regular connected topological spaces yield models of RCC, but the theorems in this paper substantially generalize this result. Additionally, the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions. Keywords: RegionConnection Calculus, Qualitative Spatial Reasoning, Boolean Connection Algebra, Mer...
Spatial Relations Between Indeterminate Regions
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2000
"... Systems of relations between regions are an important aspect of formal theories of spatial data. Examples of such relations are partof, partially overlapping, and disjoint. One particular family of systems is that based on the RegionConnection Calculus (RCC). These systems of relations were or ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
Systems of relations between regions are an important aspect of formal theories of spatial data. Examples of such relations are partof, partially overlapping, and disjoint. One particular family of systems is that based on the RegionConnection Calculus (RCC). These systems of relations were originally formulated for ideal regions, not subject to imperfections such as vagueness or indeterminacy. This paper presents two new methods for extending the relations based on the RCC from crisp regions to indeterminate regions. As a formal context for these two methods we develop an algebraic approach to spatial indeterminacy using Łukasiewicz algebras. This algebraic approach provides a generalisation of the "eggyolk" model of indeterminate regions. The two extension methods which we develop are proved to be equivalent. In particular, it is shown that it is possible to dene partof in terms of connection in the indeterminate case. This generalises a wellknown result about cris...
A family of directional relation models for extended objects
 IEEE Trans. Knowl. Data Eng
"... Abstract—In this paper, we introduce a family of expressive models for qualitative spatial reasoning with directions. The proposed family is based on the cognitive plausible conebased model. We formally define the directional relations that can be expressed in each model of the family. Then, we use ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we introduce a family of expressive models for qualitative spatial reasoning with directions. The proposed family is based on the cognitive plausible conebased model. We formally define the directional relations that can be expressed in each model of the family. Then, we use our formal framework to study two interesting problems: computing the inverse of a directional relation and composing two directional relations. For the composition operator, in particular, we concentrate on two commonly used definitions, namely, consistencybased and existential composition. Our formal framework allows us to prove that our solutions are correct. The presented solutions are handled in a uniform manner and apply to all of the models of the family. Index Terms—Spatial databases and GIS, conebased directional relations, inverse and composition operators. Ç
Part and Complement: Fundamental Concepts in Spatial Relations
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 2004
"... The spatial world consists of regions and relationships between regions. Examples of such relationships are that two regions are disjoint or that one is a proper part of the other. The formal specification of spatial relations is an important part of any formal ontology used in qualitative spatial ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
The spatial world consists of regions and relationships between regions. Examples of such relationships are that two regions are disjoint or that one is a proper part of the other. The formal specification of spatial relations is an important part of any formal ontology used in qualitative spatial reasoning or geographical information systems. Various schemes of relationships have been proposed and basic schemes have been extended to deal with vague regions, coarse regions, regions varying over time, and so on. The principal aim of this paper is not to propose further schemes, but to provide a uniform framework within which several existing schemes can be understood, and upon which further schemes can be constructed in a principled manner. This framework is based on the fundamental concepts of part and of complement. By varying these concepts, for example allowing a partof relation taking values in a lattice of truth values beyond the twovalued Boolean case, we obtain a family of schemes of spatial relations. The viability of this approach to spatial relations as parameterized by the concepts of part and complement is demonstrated by showing how it encompasses the RCC5 and RCC8 schemes as well as the case of `eggyolk regions'. The use of the approach for discrete regions is discussed briefly.
Reasoning about cardinal directions between extended objects
 Artif. Intell
"... Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualit ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NPComplete problem. For a consistent network of basic CDC constraints, our algorithm also returns a ‘canonical ’ solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n 5). 1
A 4dimensionalist mereotopology
 Formal Ontology in Information Systems
, 2004
"... ..."
(Show Context)
Representation and reasoning about general solid rectangles
 In Proceedings of the 23rd International Joint Conference on Artificial Intelligence
"... Entities in twodimensional space are often approximated using rectangles that are parallel to the two axes that define the space, socalled minimumbounding rectangles (MBRs). MBRs are popular in Computer Vision and other areas as they are easy to obtain and easy to represent. In the area of Quali ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Entities in twodimensional space are often approximated using rectangles that are parallel to the two axes that define the space, socalled minimumbounding rectangles (MBRs). MBRs are popular in Computer Vision and other areas as they are easy to obtain and easy to represent. In the area of Qualitative Spatial Reasoning, many different spatial representations are based on MBRs. Surprisingly, there has been no such representation proposed for general rectangles, i.e., rectangles that can have any angle, nor for general solid rectangles (GSRs) that cannot penetrate each other. GSRs are often used in computer graphics and computer games, such as Angry Birds, where they form the building blocks of more complicated structures. In order to represent and reason about these structures, we need a spatial representation that allows us to use GSRs as the basic spatial entities. In this paper we develop and analyze a qualitative spatial representation for GSRs. We apply our representation and the corresponding reasoning methods to solve a very interesting practical problem: Assuming we want to detect GSRs in computer games, but computer vision can only detect MBRs. How can we infer the GSRs from the given MBRs? We evaluate our solution and test its usefulness in a real gaming scenario. 1
Algebras of relations of various ranks, some current trends and applications
 Journal on Relational Methods in Computer Science 1 (2004), 2749. 26 H. Andréka, I. Németi and I. Sain, Algebraic Logic. In: Handbook of Philosophical Logic, Vol 2
, 2001
"... Abstract. Here the emphasis is on the main pillars of Tarskian structuralist approach to logic: relation algebras, cylindric algebras, polyadic algebras, and Boolean algebras with operators. We also tried to highlight the recent renaissance of these areas and their fusion with new trends related to ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. Here the emphasis is on the main pillars of Tarskian structuralist approach to logic: relation algebras, cylindric algebras, polyadic algebras, and Boolean algebras with operators. We also tried to highlight the recent renaissance of these areas and their fusion with new trends related to logic, like the guarded fragment or dynamic logic. Tarskian algebraic logic is far too broad and too fruitful and prolific by now to be covered in a short paper like this. Therefore the overview part of the paper is rather incomplete, we had to omit important directions as well as important results. Hopefully, this incompleteness will be alleviated by the accompanying paper of Tarek Sayed Ahmed [81]. The structuralist approach to a branch of learning aims for separating out the really essential things in the phenomena being studied abstracting from the accidental wrappings or details (called in computer science “syntactic sugar”). As a result of this, eventually one associates to the original phenomena (or systems) being studied streamlined elegant mathematical structures. These streamlined structures can be algebras in the sense of universal algebra, or other kinds of elegant well understood mathematical structures like e.g. spacetime geometries