Synchronization Relationships

Synchronization relationships  specify how two temporal extents relate to each other. They are essential in temporal applications, since they allow one to determine, for example, whether two events occur simultaneously or whether one precedes the other.

The synchronization relationships for temporal data correspond to the topological relationships for spatial data. They are defined in a similar way, on the basis of the concepts of the boundary, interior, and exterior.

The exterior of a temporal value is composed of all the instants of the underlying time frame that do not belong to the temporal value. On the other hand, the interior of a temporal value is composed of all its instants that do not belong to the boundary. The boundary is defined for the different temporal data types as follows. An instant has an empty boundary. The boundary of an interval consists of its start and end instants. The boundary of a ComplexTime value is (recursively) defined by the union of the boundaries of its components that do not intersect with other components.

 

synchronization relationships

meets: Two temporal values meet if they intersect in an instant but their interiors do not. Note that two temporal values may intersect in an instant but do not meet.

overlaps: Two temporal values overlap if their interiors intersect and their intersection is not equal to either of them.

contains/inside: contains and inside are symmetric predicates: a contains b if and only if b inside a. A temporal value contains another one if the interior of the former contains all instants of the latter.

covers/coveredBy: covers and coveredBy are symmetric predicates: a covers b if and only if b coveredBy a. A temporal value covers another one if the former includes all instants of the latter. This means that the former contains the latter, as defined above, but without the restriction that the boundaries of the temporal extents do not intersect. As a particular case, the two temporal values may be equal.

disjoint/intersects: disjoint and intersects are inverse temporal predicates: when one applies, the other does not. Two temporal values are disjoint if they do not share any instant.

equals: Two temporal values are equal if every instant of the first value belongs also to the second and conversely.

starts/finishes: A temporal value starts another if the first instants of the two values are equal. Similarly, a temporal value finishes another if the last instants of the two values are equal.

precedes/succeeds: A temporal value precedes another if the last instant of the former is before the first instant of the latter. Similarly, a temporal value succeeds another if the first instant of the former is later than the last instant of the latter.