Results 1  10
of
56
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 ..."
Abstract

Cited by 618 (31 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 204 (17 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].
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus&quo ..."
Abstract

Cited by 125 (22 self)
 Add to MetaCart
(Show Context)
The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC8 that contains all base relations. Further, we show that for this subset pathconsistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the socalled Region Connecti...
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 ..."
Abstract

Cited by 103 (16 self)
 Add to MetaCart
(Show Context)
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...
A Connection Based Approach to Commonsense Topological Description and Reasoning
, 1995
"... The standard mathematical approaches to topology, pointset topology and algebraic topology, treat points as the fundamental, undefined entities, and construct extended spaces as sets of points with additional structure imposed on them. Pointset topology in particular generalises the concept of ..."
Abstract

Cited by 52 (9 self)
 Add to MetaCart
The standard mathematical approaches to topology, pointset topology and algebraic topology, treat points as the fundamental, undefined entities, and construct extended spaces as sets of points with additional structure imposed on them. Pointset topology in particular generalises the concept of a `space' far beyond its intuitive meaning. Even algebraic topology, which concentrates on spaces built out of `cells' topologically equivalent to ndimensional discs, concerns itself chiefly with rather abstract reasoning concerning the association of algebraic structures with particular spaces, rather than the kind of topological reasoning which is required in everyday life, or which might illuminate the metaphorical use of topological concepts such as `connection' and `boundary'. This paper explores an alternative to these approaches, RCC theory, which takes extended spaces (`regions') rather than points as fundamental. A single relation, C (x; y) (read `Region x connects with reg...
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 50 (7 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
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 ..."
Abstract

Cited by 49 (21 self)
 Add to MetaCart
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.
Efficient methods for qualitative spatial reasoning
 Proceedings of the 13th European Conference on Artificial Intelligence
, 1998
"... The theoretical properties of qualitative spatial reasoning in the RCC8 framework have been analyzed extensively. However, no empirical investigation has been made yet. Our experiments show that the adaption of the algorithms used for qualitative temporal reasoning can solve large RCC8 instances, ..."
Abstract

Cited by 49 (14 self)
 Add to MetaCart
The theoretical properties of qualitative spatial reasoning in the RCC8 framework have been analyzed extensively. However, no empirical investigation has been made yet. Our experiments show that the adaption of the algorithms used for qualitative temporal reasoning can solve large RCC8 instances, even if they are in the phase transition region  provided that one uses the maximal tractable subsets of RCC8 that have been identified by us. In particular, we demonstrate that the orthogonal combination of heuristic methods is successful in solving almost all apparently hard instances in the phase transition region up to a certain size in reasonable time.
A Cognitive Assessment of Topological Spatial Relations: Results from an Empirical Investigation
 IN PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON SPATIAL INFORMATION THEORY (COSIT'97), VOLUME 1329 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1997
"... Whether or not a formal approach to spatial relations is a cognitively adequate (the term will be explicated in this paper) model of human spatial knowledge is more often based on the intuition of the researchers than on empirical data. In contrast, the research reported here is concerned with an ..."
Abstract

Cited by 48 (11 self)
 Add to MetaCart
Whether or not a formal approach to spatial relations is a cognitively adequate (the term will be explicated in this paper) model of human spatial knowledge is more often based on the intuition of the researchers than on empirical data. In contrast, the research reported here is concerned with an empirical assessment of one of the three general classes of spatial relations, namely topological knowledge. In the reported empirical investigation, subjects had to group numerous spatial configurations consisting of two circles with respect to their similarity. As is well known, such tasks are solved on the basis of underlying spatial concepts. The results were compared with the RCCtheory and Egenhofer's approach to topological relations and support the assumption that both theories are cognitively adequate in a number of important aspects.
Computational Properties of Qualitative Spatial Reasoning: First Results
 KI95: ADVANCES IN ARTIFICIAL INTELLIGENCE
, 1995
"... While the computational properties of qualitative temporal reasoning have been analyzed quite thoroughly, the computational properties of qualitative spatial reasoning are not very well investigated. In fact, almost no completeness results are known for qualitative spatial calculi and no computati ..."
Abstract

Cited by 38 (4 self)
 Add to MetaCart
While the computational properties of qualitative temporal reasoning have been analyzed quite thoroughly, the computational properties of qualitative spatial reasoning are not very well investigated. In fact, almost no completeness results are known for qualitative spatial calculi and no computational complexity analysis has been carried out yet. In this paper, we will focus on the socalled RCC approach and use Bennett's encoding of spatial reasoning in intuitionistic logic in order to show that consistency checking for the topological base relations can be done efficiently. Further, we show that pathconsistency is sufficient for deciding global consistency. As a sideeffect we prove a particular fragment of propositional intuitionistic logic to be tractable.