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Definition:

Relation that specifies temporal constraints between pairs of Process Steps in a Sequence following Allen's interval algebra. A Sequence in the Process Model is a Control Construct in which the elements of the sequence (i.e. Process Steps) have positions on a timeline with respect to each other.

In Allen's interval algebra between Process Steps a and b there are seven possible relations. All but one are asymmetric and thus have a converse. The exception is the situation where two intervals are coextensive. Then the relation and its converse are the same, namely equal, which is an equivalence relation.

Explanatory Notes:

Here are the relations in Allen's interval algebra:

*a* precedes *b* (p) and *b* is preceded by *a* (P)*a* meets *b* (m) and *b* is met by *a* (M)*a* overlaps *b* (o) and *b* is overlapped by *a* (O)*a* is finished by *b* (F) and *b* finishes *a* (f)*a* contains B (D) and *b* is during *a* (d)*a* starts *b* (s) and *b* is started by *a* (S)*a* and *b* equal (e) each other

There is no guarantee that a set of pairs will be tractable. A simple example of a collection of relations and intervals that is not tractable is three intervals *a*, *b*, and *c* such that *a(p)b*, *b(p)c*, and *c(p)a* (each precedes the next, and the last precedes the first). There are no definite intervals for which all these relations can hold. In this event we say that the collection is **unsatisfiable**.

That being said certain collections of pairwise relations are in fact **composable**. Composition is not commutative but is both left and right associative, and distributes over union. Collections that are composable support inference over their pairs. In fact, certain mixes of pairwise relations have been found to be composable over a collection. These mixes are call **tractable subalgebras**. Eighteen of these have been identified.

For a more in-depth discussion see http://www.ics.uci.edu/~alspaugh/cls/shr/allen.html.

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Name | Cardinality | Datatype | Description |
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totality | 1..1 | Controlled Vocabulary to specify whether the relation is total, partial or unknown. |

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