||This article may be too technical for most readers to understand. (October 2012)|
Spatial–temporal reasoning is an area of computer science focused on navigating and understanding time and space. An emphasis has been on qualitative spatial-temporal reasoning which is based on qualitative abstractions of temporal and spatial aspects of the common-sense background knowledge on which our human perspective of physical reality is based. Methodologically, qualitative constraint calculi restrict the vocabulary of rich mathematical theories dealing with temporal or spatial entities such that specific aspects of these theories can be treated within decidable fragments with simple qualitative (non-metric) languages. Contrary to mathematical or physical theories about space and time, qualitative constraint calculi allow for rather inexpensive reasoning about entities located in space and time. For this reason, the limited expressiveness of qualitative representation formalism calculi is a benefit if such reasoning tasks need to be integrated in applications. For example, some of these calculi may be implemented for handling spatial GIS queries efficiently and some may be used for navigating, and communicating with, a mobile robot.
Examples of temporal calculi include Allen's interval algebra, and Vilain's & Kautz's point algebra. The most prominent spatial calculi are mereotopological calculi, Frank's cardinal direction calculus, Freksa's double cross calculus, Egenhofer and Franzosa's 4- and 9-intersection calculi, Ligozat's flip-flop calculus, various region connection calculi (RCC), and the Oriented Point Relation Algebra. Recently, spatio-temporal calculi have been designed that combine spatial and temporal information. For example, the spatiotemporal constraint calculus (STCC) by Gerevini and Nebel combines Allen's interval algebra with RCC-8. Moreover, the qualitative trajectory calculus (QTC) allows for reasoning about moving objects.
Most of these calculi can be formalized as abstract relation algebras, such that reasoning can be carried out at a symbolic level. For computing solutions of a constraint network, the path-consistency algorithm is an important tool.
- J. Renz, B. Nebel, Qualitative Spatial Reasoning using Constraint Calculi, in: M. Aiello, I. Pratt-Hartmann, J. van Benthem (eds.): Handbook of Spatial Logics, Springer 2007.
- M. Vilain, H. Kautz, P. van Beek, Constraint propagation algorithms for temporal reasoning: A Revised Report, 1987.