This section describes common constraints in scheduling, namely, precedence constraints. Informally, these constraints restrict the relative position of interval variables in a solution. For instance a precedence constraint can model the fact that an activity a must end before activity b starts (optionally with some minimum delay z). If one or both of the interval variables of the precedence constraint is absent, then the precedence is systematically considered to be true, and, thus, it does not impact the schedule.

More formally, the semantics of the relation TC(, , z) on a pair of fixed intervals a, b and for a value z depending on the constraint type TC is given in Table 1.

Presence status of interval variables can be further restricted by logical constraints. The presence constraint  presenceOf(a) states that a given interval variable must be present. Of course, this constraint may be used in logical constraints; for example, there may be two optional intervals a and b, but if interval a is present then b must be present too. This can be modeled by the constraint presenceOf(a)  presenceOf(b).

The semantics of the presence constraint on a fixed interval is just:

presenceOf() x()