As previously mentioned, there are many possible relationships between two intervals: one interval can lie completely before the other, both intervals can start and/or end at the same time, they can overlap each other etc. Temporal joins can be classified according to the type of interval relationship that its join condition is based on. Table 11.1 shows a set of join conditions. We treat them as elementary for the three reasons spelled out in section 4.1.
Please note that the after join is redundant within this list as
Allen's interval relationships [Allen, 1983] are frequently considered to be elementary too. However, they lead to more complex expressions when translated into relationships between intervals' start- and endpoints. This makes it more difficult to decompose complex temporal join conditions into elementary ones. For that reason we opt for the set presented in table 11.1.
Additional constraints are: 
with 
.Relationship
Join Name & Symbol
Condition
Informal Description
start
start join:
r.ts = q.ts
same timestamp startpoints
finish
finish join:
r.te = q.te
same timestamp endpoints
meet
meet join:
r.te = q.ts
timestamp of r ends where timestamp of q starts, i.e. they meet.
before
before join:
r.te < q.ts
timestamp of r comes before q's timestamp
after
after join:
r.ts > q.te
timestamp of r comes after q's timestamp
left-overlap
left-overlap join:
startpoint of r's timestamp lies within q's timestamp
right-overlap
right-overlap join:
endpoint of r's timestamp lies within q's timestamp
