Allen's interval algebra

The Allen- calculus, also known as Allen's interval algebra is a logic for representing temporal relationships and logical Close, which was introduced in 1983 by James F. Allen.

The calculus defines possible temporal relationships between intervals, and describes an algorithm to time based on descriptions of events, draw inferences between them can.

Formal Description

Relations

With the help of the imaged 13 relations, it is possible to describe all the possible relationships between exactly two intervals. The relations include the inverse.

Hereby given facts can now be formalized and then processed automatically.

The given sentence

Leads to the following formalization according to Allen- calculus:

Links of intervals

Which are made to close correlations between time intervals defined the Allen calculus a composition table, which enables the basis of given relations between and and between and on the relation of and close.

So it can be said for the example given, that must apply.

Extensions

The Allen- calculus can be used not only for the description of temporal intervals, but it is also suitable for the representation of spatial conditions. To this end, the importance of the relations is changed and now describes the position of two objects to each other.

Thereby, three-dimensional objects can be described in which the correlation of each coordinate are listed individually.

Another possibility for spatial reasoning provides the RCC8 calculus.

Implementation

• A simple Java library which implements the Allen- calculus, including the path -consistency method