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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 ..."
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Cited by 264 (18 self)
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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].
A Temporal Description Logic for Reasoning about Actions and Plans
- Journal of Artificial Intelligence Research
, 1998
"... A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The tempo ..."
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Cited by 98 (20 self)
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A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered #rst: it is the composition of a temporal logic TL # able to express interval temporal networks # together with the non-temporal logic F # a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF . The former adds disjunction both at...
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 71 (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
Spatial Reasoning with Topological Information
- Ph.D. thesis, Institut fur Informatik, Albert-Ludwigs-Universitat Freiburg
, 1998
"... . This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the re ..."
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Cited by 62 (2 self)
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. This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the required dimension of the applied space. Further, it includes computational issues, e.g., how hard is it to reason with the calculus and are there efficient algorithms. Finally, we also address cognitive issues, i.e., is the calculus cognitively adequate. 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. Different aspects of space can be treated in a qualitative way. Among others there are approaches considering orientation, distance, shape, topology, and combinations of these. A summary o...
EXPTIME tableaux for ALC
- ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semi-structured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIME-complete. Second, experiments in automated reaso ..."
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Cited by 61 (4 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semi-structured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIME-complete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACE-complete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on tree-automata, which are used to prove EXPTIME-completeness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.
Spatio-Temporal Predicates
- IEEE Transactions on Knowledge and Data Engineering
, 1999
"... AbstractÐThis paper investigates temporal changes of topological relationships and thereby integrates two important research areas: First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial information over time. We investigate ..."
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Cited by 57 (15 self)
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AbstractÐThis paper investigates temporal changes of topological relationships and thereby integrates two important research areas: First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial information over time. We investigate spatio-temporal predicates, which describe developments of well-known spatial topological relationships. A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary spatial predicates and sequential composition. We compare our framework with two other possible approaches: one is based on the observation that spatio-temporal objects correspond to three-dimensional spatial objects for which existing topological predicates can be exploited. The other approach is to consider possible transitions between spatial configurations. These considerations help to identify a canonical set of spatio-temporal predicates. Index TermsÐTime in geographic information, spatio-temporal data types, representation of spatio-temporal objects, changes of spatial predicates, developments of spatial objects. 1
Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning
- APPLIED INTELLIGENCE
, 2000
"... In this paper we advocate the use of multi-dimensional modal logics as a framework for knowledge representation and, in particular, for representing spatiotemporal information. We construct a two-dimensional logic capable of describing topological relationships that change over time. This logic, ca ..."
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Cited by 53 (6 self)
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In this paper we advocate the use of multi-dimensional modal logics as a framework for knowledge representation and, in particular, for representing spatiotemporal information. We construct a two-dimensional logic capable of describing topological relationships that change over time. This logic, called PSTL (Propositional Spatio-Temporal Logic) is the Cartesian product of the well-known temporal logic PTL and the modal logic S4u , which is the Lewis system S4 augmented with the universal modality. Although it is an open problem whether the full PSTL is decidable, we show that it contains decidable fragments into which various temporal extensions (both point-based and interval based) of the spatial logic RCC-8 can be embedded. We consider known decidability and complexity results that are relevant to computation with muli-dimensional formalisms and discuss possible directions for further research.
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 ..."
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Cited by 52 (10 self)
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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 RCC-theory and Egenhofer's approach to topological relations and support the assumption that both theories are cognitively adequate in a number of important aspects.
A Canonical Model of the Region Connection Calculus
- Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR-98
, 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 ..."
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Cited by 51 (5 self)
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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 RCC-8 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...
