TC operators are based on six fundamental binary relations among regions: before, after, in, contains, overlapsstart, and, overlapsend. (Similar relations on time intervals were defined in [2].) The region relations are defined as follows:
[b_{1},e_{1}] before [b_{2},e_{2}]  if and only if e_{1} <= b_{2} 
[b_{1},e_{1}] after [b_{2},e_{2}]  if and only if e_{2} <= b_{1} 
[b_{1},e_{1}] in [b_{2},e_{2}]  if and only if b_{2} <= b_{1} and e_{1} <= e_{2} 
[b_{1},e_{1}] contains [b_{2},e_{2}]  if and only if b_{1} <= b_{2} and e_{2} <= e_{1} 
[b_{1},e_{1}] overlapsstart [b_{2},e_{2}]  if and only if b_{1} <= b_{2} and e_{1} <= e_{2} 
[b_{1},e_{1}] overlapsend [b_{2},e_{2}]  if and only if b_{2} <= b_{1} and e_{2} <= e_{1} 

Figure 2: Fundamental region relations in an example string. Regions
A through F are related to region R as follows:
A before R; B overlapsstart R; C contains R; D
in R; E overlapsend R; and F after R.

justbefore  = before and overlapsstart 
justafter  = after and overlapsend 
atstartof  = in and overlapsstart 
atendof  = in and overlapsend 
startswith  = contains and overlapsstart 
endswith  = contains and overlapsend 

Figure 3: Region relations with coincident endpoints. Regions A
through F are related to region R as follows: A
justbefore R; B atstartof R; C atendof R; D
startswith R; E endswith R; and F justafter R.

overlaps =  in and contains and 
overlapsstart and overlapsend 