i) The constraints [I1 (ec1 ∨ ¬ec1) I2] and [I1 (ec2 ∨ ¬ec2) I2] can be expressed as disjunctive metric constraints on the same pairs of time-points, ii) The constraints [I1 ¬(ec1 ∧ ec2) I2] and [I1 ¬(¬ec1 ∧ ¬ec2) I2] can be expressed as a mutual exclusion among the associated labels of the above point-based constraints. That is, as a set of I-L-Sets.
We present a simple example to illustrate these conclusions. For instance, (I1 {before after} I2)
can be expressed by means of constraints among the time points I1
-, I1
+, I2
-and I2
+, as:
[I1 {b a} I2] ≡ (I1
+{(0 ∞){Rb1}} I2
-) ∨ (I1
-{(-∞ 0){Ra1}} I2
+).

Thus, when intervals are represented by means of their ending points Ii
+Ii
-, an interval-based constraint gives rise to disjunctive constraints between different pairs of time points (i.e.: non-binary constraints). These non-binary constraints can be represented as I-L-Sets. Thus, according to the above expression (e2),
[I1 {b a} I2] ≡ [I1 (b ∨ ¬b) I2] ∧ [I1 (a ∨ ¬a) I2] ∧ [I1 ¬(b ∧ a) I2] ∧ [I1 ¬(¬b ∧ ¬a) I2],
we have:
I1 before I2 ⇔ I1
+{(0 ∞){Rb1}} I2
-,
I1 ¬before I2 ⇔ I1
+{(-∞ 0]{Rb2}} I2
-,

$$\begin{array}{l l}{{\mathrm{I_{1}~a t e r~I_{2}}}}&{{\Leftrightarrow}}&{{\mathrm{I_{1}^{-}\left\{\left(-\infty\,0\right)_{\left\{\mathrm{Ra11}\right\}}\right\}\,I_{2}^{+},}}}\\ {{\mathrm{I_{1}~-a t e r~I_{2}}}}&{{\Leftrightarrow}}&{{\mathrm{I_{1}^{-}\left\{\left[0\,\infty\right)_{\left\{\mathrm{Ra2}\right\}}\right\}\,I_{2}^{+}.}}}\end{array}$$

Therefore, [I1 {b a} I2] can be expressed as:
[I1
+{(0 ∞){Rb1} (-∞ 0]{Rb2}} I2
-] ∧ [I1
-{(-∞ 0){Ra1} [0 ∞){Ra2}} I2
+] ∧

¬ [ (I1
+{(0 ∞){Rb1}} I2
-) ∧ (I1
-{(-∞ 0){Ra1}} I2
+) ] ∧ 

$\neg\left[\;\left(\mathrm{I}_{1}^{+}\right.\right\{\right]$
$\downarrow$
+{(-∞ 0]{Rb2}} I2
-) ∧ (I1
-{[0 ∞){Ra2}} I2
+) ],
which is equivalent to (by using the labels associated to each elemental constraint):
[I1
+{(0 ∞){Rb1} (-∞ 0]{Rb2}} I2
-] ∧ [I1
-{(-∞ 0){Ra1} [0 ∞){Ra2}} I2
+]
and {Rb1 Ra1},{Rb2 Ra2} are I-L-Sets, such that one and only one disjunctive symbolic constraint holds.

Thus, symbolic constraints between intervals can be represented by means of: (i) a set of disjunctive metric constraints between time-points, and *(ii)* a set of I-L-Sets. In Table 1, the equivalent metric constraints between interval ending time points for each elemental interval-based constraint are detailed. According to this table, the following steps allow us to represent disjunctive symbolic constraints between intervals by means of disjunctive metric constraints between interval ending points and I-L-Sets:
i) Each interval Ii is represented by means of its ending points Ii
+, Ii
-. By default, (Ii
-{(0, ∞){R0}}

Ii
+) holds.

ii) A symbolic constraint between two intervals (Ii cij Ij) is composed of a disjunctive set of
(from 1 to 13) elemental symbolic constraints cij={ecij.k}⊆{b, m, o, d, s, f, e, bi, mi, oi, di, si, fi}.
iii) Each elemental symbolic constraint ec∈{b, m, o, d, s, f, e, bi, mi, oi, di, si, fi} is represented