ALLEN RELATIONSHIP AND OTHER QUERIES - Managing Time in Relational Databases - page 322

The predicate for this relationship, as it holds between two
time periods expressed as pairs of dates using the closed-open
convention, is:
(eff_end_dt 1 < eff_beg_dt 2 )
It says that after P 1 ends, there is at least one clock tick before
P 2 begins. For example, consider the case where eff_end_dt 1 is
5/13/2014 and eff_beg_dt 2 is 5/14/2014. Because of the closed-
open convention, the last clock tick in P 1 is 5/12/2014, and so
there is one clock tick gap between the two time periods, that
clock tick being 5/13/2014.
The inverse of this relationship is: P 1 [before 1 ]P 2 . In the
superscripted relationship, the first time period is the later one.
The predicate for this relationship, as it holds between two time
periods expressed as pairs of dates using the closed-open
convention, is:
(eff_beg_dt 1 > eff_end_dt 2 )
It says that before P 1 begins, there is at least one clock tick
after P 2 ends. For example, consider the case where eff_beg_dt 1
is 5/14/2014 and eff_end_dt 2 is 5/13/2014. Because of the
closed-open convention, the last clock tick in P 2 is 5/12/2014,
and so there is one clock tick gap between the two time periods,
that clock tick being 5/13/2014.
Throughout this topic, if it isn't important which time period
comes first, we will simply say that the two time periods are non-
contiguous.
This is a particularly useful pair of relationships because they
distinguish episodes of the same object from one another.
Two adjacent versions—versions of an object with no other ver-
sion of the same object between them—belong to different
episodes just in case the earlier one is [before] the later one.
Of two adjacent episodes of the same object, one is [before]
the other, and the other is [before 1 ] the former.
Consider the following request for information: which
policies ended at least one date before the Diabetes Manage-
ment Wellness Program for 2009 began?
The SQL written to fulfill this request is:
SELECT * FROM V_Allen_Example
WHERE pol_epis_end_dt < wp_eff_beg_dt
P 1 [meets] P 2
This is a pair of relationships, one the inverse of the other.
In the non-superscripted relationship, the first time period is
the earlier one.