article

Determining Consistency of Topological Relations

Author:

Brandon BennettAuthors Info & Claims

Constraints, Volume 3, Issue 2/3

Pages 213 - 225

https://doi.org/10.1023/A:1009729828056

Published: 01 June 1998 Publication History

Abstract

This paper examines the problem of testing consistency of sets of topological relations which are instances of the RCC-8 relation set Leeds92a. Representations of these relations as constraints within a number of logical frameworks are considered. It is shown that, if the arguments of the relations are interpreted as non-empty open sets within an arbitrary topological space, a complete consistency checking procedure can be provided by means of a composition table. This result is contrasted with the case where regions are required to be planar and bounded by Jordan curves, for which the consistency problem is known to be NP-hard.

In order to investigate the completeness of compositional reasoning, the notion of k -compactness of a set of relations w.r.t. a theory is introduced. This enables certain consistency properties of relational networks to be examined independently of any specific interpretation of the domain of entities constrained by the relations.

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Cited By

Bodirsky MWölfl S(2011)RCC8 is polynomial on networks of bounded treewidthProceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two10.5555/2283516.2283526(756-761)Online publication date: 16-Jul-2011
https://dl.acm.org/doi/10.5555/2283516.2283526
Li JKowalski TRenz JLi S(2008)Combining binary constraint networks in qualitative reasoningProceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence10.5555/1567281.1567394(515-519)Online publication date: 27-Jun-2008
https://dl.acm.org/doi/10.5555/1567281.1567394
Schockaert SDe Cock MCornelis CKerre E(2008)Fuzzy region connection calculusInternational Journal of Approximate Reasoning10.1016/j.ijar.2007.10.00148:1(314-331)Online publication date: 1-Apr-2008
https://dl.acm.org/doi/10.1016/j.ijar.2007.10.001
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Determining Consistency of Topological Relations
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cover image Constraints

Constraints Volume 3, Issue 2/3

June 1998

123 pages

ISSN:1383-7133

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Copyright © Copyright © 1998 Kluwer Academic Publishers.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 June 1998

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Cited By

Bodirsky MWölfl S(2011)RCC8 is polynomial on networks of bounded treewidthProceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two10.5555/2283516.2283526(756-761)Online publication date: 16-Jul-2011
https://dl.acm.org/doi/10.5555/2283516.2283526
Li JKowalski TRenz JLi S(2008)Combining binary constraint networks in qualitative reasoningProceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence10.5555/1567281.1567394(515-519)Online publication date: 27-Jun-2008
https://dl.acm.org/doi/10.5555/1567281.1567394
Schockaert SDe Cock MCornelis CKerre E(2008)Fuzzy region connection calculusInternational Journal of Approximate Reasoning10.1016/j.ijar.2007.10.00148:1(314-331)Online publication date: 1-Apr-2008
https://dl.acm.org/doi/10.1016/j.ijar.2007.10.001
Cristani MHirsch R(2004)The complexity of constraint satisfaction problems for small relation algebrasArtificial Intelligence10.1016/j.artint.2004.02.003156:2(177-196)Online publication date: 1-Jul-2004
https://dl.acm.org/doi/10.1016/j.artint.2004.02.003
Balbiani PCondotta J(2002)Computational Complexity of Propositional Linear Temporal Logics Based on Qualitative Spatial or Temporal ReasoningProceedings of the 4th International Workshop on Frontiers of Combining Systems10.5555/646821.706727(162-176)Online publication date: 8-Apr-2002
https://dl.acm.org/doi/10.5555/646821.706727
Bennett BCohn AWolter FZakharyaschev M(2002)Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal ReasoningApplied Intelligence10.1023/A:102008323150417:3(239-251)Online publication date: 3-Sep-2002
https://dl.acm.org/doi/10.1023/A%3A1020083231504

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