Results 11  20
of
111
Spatiotemporal representation and reasoning based on RCC8
 In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000
, 2000
"... this paper is to introduce a hierarchy of languages intended for qualitative spatiotemporal representation and reasoning, provide these languages with topological temporal semantics, construct effective reasoning algorithms, and estimate their computational complexity. ..."
Abstract

Cited by 60 (10 self)
 Add to MetaCart
(Show Context)
this paper is to introduce a hierarchy of languages intended for qualitative spatiotemporal representation and reasoning, provide these languages with topological temporal semantics, construct effective reasoning algorithms, and estimate their computational complexity.
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 55 (8 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...
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 52 (20 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.
A Canonical Model of the Region Connection Calculus
 Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR98
, 1997
"... Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dim ..."
Abstract

Cited by 51 (5 self)
 Add to MetaCart
Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dimension as used by the Region Connection Calculus. In this paper we present a canonical model which allows regions and relations between them to be represented as points of the topological space and information about their neighbourhoods. With this formalism we are able to prove that whenever a set of RCC8 formulas is consistent there exists a realization in any dimension, even when the regions are constrained to be (sets of) polytopes. For three and higher dimensional space this is also true for internally connected regions. Using the canonical model we give algorithms for generating consistent scenarios. 1 Introduction The Region Connection Calculus (RCC) is a topological approach t...
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 51 (12 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 Hierarchical Representation of Qualitative Shape based on Connection and Convexity
 Proc COSIT95, LNCS
, 1995
"... . In this paper we consider the problem of representing the shape of a region, qualitatively, within a logical theory of space. Using just two primitive notions, that of two regions connecting, and the convex hull of a region, a wide variety of concave shapes can be distinguished. Moreover, by a ..."
Abstract

Cited by 46 (7 self)
 Add to MetaCart
(Show Context)
. In this paper we consider the problem of representing the shape of a region, qualitatively, within a logical theory of space. Using just two primitive notions, that of two regions connecting, and the convex hull of a region, a wide variety of concave shapes can be distinguished. Moreover, by applying the technique recursively to the inside of a region (i.e. that part of the convex hull not occupied by the region itself), a hierarchical representation at varying levels of granularity can be obtained. 1 Introduction In this paper we consider the problem of representing the shape of a region, qualitatively, within a logical theory of space, known as RCC theory (Randell and Cohn 1989, Randell, Cui and Cohn 1992, Cohn, Randell and Cui 1994). This logic originally had just one primitive notion, C(x; y), that of two regions x and y connecting. However, to make an initial attack on this problem, the notion of the convex hull of a region, conv(x) was introduced (see figure 1); this a...
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 42 (5 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.
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 ..."
Abstract

Cited by 39 (12 self)
 Add to MetaCart
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
RegionBased Qualitative Geometry
, 2000
"... We present a highly expressive logical language for describing qualitative configurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as pri ..."
Abstract

Cited by 35 (14 self)
 Add to MetaCart
We present a highly expressive logical language for describing qualitative configurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We show that our theory is categorical: all models are isomorphic to a classical interpretation in terms of Cartesian spaces over R. We investigate
An AutomataTheoretic Approach to Constraint LTL
, 2003
"... We consider an extension of lineartime temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automatatheoretic ..."
Abstract

Cited by 32 (7 self)
 Add to MetaCart
We consider an extension of lineartime temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automatatheoretic proof of a result of [BC02] when the constraint system D satisfies the completion property. Our decision procedures extend easily to handle extensions of the logic with past operators and constants, as well as an extension of the temporal language itself to monadic second order logic. Finally, we show that the logic...