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Journal of Logic and Computation Advance Access published online on June 26, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp025
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Qualitative Temporal and Spatial Reasoning Revisited1

Manuel Bodirsky

Laboratoire d’informatique (LIX, CNRS UMR 6171), École Polytechnique, Paris-Palaiseau, France.
E-mail: bodirsky{at}lix.polytechnique.fr

Hubie Chen

Departament de Tecnologies de la Informació i les Comunicacions, Universitat Pompeu Fabra, Barcelona, Spain.
E-mail: hubie.chen{at}upf.edu

Received 14 November 2007.


  Abstract

Establishing local consistency is one of the main algorithmic techniques in temporal and spatial reasoning. Acentral question for the various proposed temporal and spatial constraint languages is whether local consistency implies global consistency. Showing that a constraint language {Gamma} has this ‘local-to-global’ property implies polynomial-time tractability of the constraint language, and has further pleasant algorithmic consequences. In the present article, we study the ‘local-to-global’ property by making use of a recently established connection of this property with universal algebra. Roughly speaking, the connection shows that this property is equivalent to the presence of a so-called quasi near-unanimity (QNU) polymorphism of the constraint language. We obtain new algorithmic results and give very concise proofs of previously known theorems. Our results concern well-known and heavily studied formalisms such as the point algebra, Allen's interval algebra and the spatial reasoning language RCC-5.

Keywords: Temporal reasoning; spatial reasoning; constraint satisfaction; computational complexity; consistency; nearunanimity operations

1 An extended abstract of this article appeared in the 16th EACSL Annual Conference on Computer Science and Logic (CSL 2007).


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