Spatio-temporal reasoning

Spatial-temporal reasoning is the ability to visualize spatial patterns and mentally manipulate them over a time-ordered sequence of spatial transformations.

This ability is important for generating and conceptualizing solutions to multi-step problems that arise in areas such as architecture, engineering, science, mathematics, art, games, and everyday life.

While some visual thinkers (who account for around 60% of the general population) also have good spatial-temporal reasoning this does not make spatial-temporal reasoning exclusive to those who "think in pictures".

Spatial-temporal reasoning can have as much or more to do with one of the other 5 main modes of thought: the logical (mathematical/systems) style of thought.

Kinesthetic learners (physical learners who learn through body mapping and physical patterning) are highly developed in spatial awareness and may also visualize spatial patterns and movement direction without being predominantly those who 'think in pictures'. The same is true of logical thinkers (mathematical/systems thinking) who think in patterns and relationships and may work diagrammatically without this being pictorially and, as such, may have excellent spatial-temporal reasoning yet not necessarily be strong visual thinkers at all.

Spatial-temporal reasoning is also studied in computer science. It aims at describing the common-sense background knowledge on which our human perspective on the 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 the so-called point algebra, Allen's Interval Algebra, and Villain's point-interval calculus. 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, and various region connection calculi (RCC). Recently, spatio-temporal calculi have been designed. For example, the Spatio-temporal 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.