TC operators are based on six fundamental binary relations among regions: before, after, in, contains, overlaps-start, and, overlaps-end. (Similar relations on time intervals were defined in [2].) The region relations are defined as follows:
[b1,e1] before [b2,e2] | if and only if e1 <= b2 |
[b1,e1] after [b2,e2] | if and only if e2 <= b1 |
[b1,e1] in [b2,e2] | if and only if b2 <= b1 and e1 <= e2 |
[b1,e1] contains [b2,e2] | if and only if b1 <= b2 and e2 <= e1 |
[b1,e1] overlaps-start [b2,e2] | if and only if b1 <= b2 and e1 <= e2 |
[b1,e1] overlaps-end [b2,e2] | if and only if b2 <= b1 and e2 <= e1 |
|
Figure 2: Fundamental region relations in an example string. Regions
A through F are related to region R as follows:
A before R; B overlaps-start R; C contains R; D
in R; E overlaps-end R; and F after R.
|
just-before | = before and overlaps-start |
just-after | = after and overlaps-end |
at-start-of | = in and overlaps-start |
at-end-of | = in and overlaps-end |
starts-with | = contains and overlaps-start |
ends-with | = contains and overlaps-end |
|
Figure 3: Region relations with coincident endpoints. Regions A
through F are related to region R as follows: A
just-before R; B at-start-of R; C at-end-of R; D
starts-with R; E ends-with R; and F just-after R.
|
overlaps = | in and contains and |
overlaps-start and overlaps-end |