Information Technology Reference
In-Depth Information
2
Background
Interval algebra [3] provides a means to represent time intervals associated with
actions and entities and to computationally reason about their relationships. It defines
the possible relations that can hold between two time intervals (see Table 1). These
relations are mutually exclusive, in that only one is needed to describe the relative
temporal placement of any two time intervals. Interval algebra assumes that the
beginning and ending points (signified with “
” and “+” respectively) of an interval
do not coincide. For each entry in Table 1, the first line shows the basic relation and
the second line shows its inverse relation.
−
Table 1.
Basic temporal relationships
P
REDICATE
F
ORM
R
ELATION ON
E
NDPOINTS
R
ELATION
S
YMBOL
P
ICTORIAL
M
EANING
x
y
x
before
y
y
after
x
BEFORE
(
x,y
)
AFTER
(
y,x
)
<
>
(
x
+
<
y
−
)
x
y
x
equals
y
y
equals
x
EQUALS
(
x,y
)
EQUALS
(
y,x
)
=
=
(
x
−
=
y
−
)
∧
(
x
+
=
y
+
)
x y
x
meets
y
y
met by
x
MEETS
(
x,y
)
MET
_
BY
(
y,x
)
m
mi
x
+
=
y
−
x
(
x
(
x
+ >
y
−) ∧
(
x
+ <
y
+)
−
<
y
−
)
∧
x
overlaps
y
y
overlapped by
x
OVERLAPS
(
x,y
)
OVERLAPPED
_
BY
(
y,x
)
o
oi
y
x
y
x
during
y
y
includes
x
DURING
(
x,y
)
INCLUDES
(
y,x
)
d
di
(
x
−
>
y
−
)
∧
(
x
+
<
y
+
)
x
x
starts
y
y
started by
x
STARTS
(
x,y
)
STARTED
_
BY
(
y,x
)
s
si
(
x
−
=
y
−
)
∧
y
(
x
+
<
y
+
)
x
y
x
finishes
y
y
finished by
x
FINISHES
(
x,y
)
FINISHED
_
BY
(
y,x
)
f
fi
(
x
−
>
y
−
)
∧
(
x
+
=
y
+
)
A set of time intervals and their required or allowed interrelationships can be
represented using a directed graph (also known as an
interval algebra network
, or
IA
network
), in which each vertex represents an individual time interval and each
directed edge represents the relationship(s) between a pair of vertices.
