{Rkl.y}} and {Rkl.y} Χ {{Rij.1, Rij.2, ....., Rij.p}-{Rij.x}} should be added to the set of I-L-Sets.

For instance, let's see the Example 2 of Section 4.4 (Figure 10):

- To represent that *'John goes to work by car and Fred goes to work walking'* is not possible,
{R1 R5} should be asserted as an I-L-Set.

- To represent that *'if John goes to work by car then Fred goes to work walking'*, {R1 R3} and
{R1 R4} should be asserted as I-L-Sets.

- To represent that *'if John goes to work by car then Fred goes to work walking, and vice versa'*,
{R1 R3}, {R1 R4} and {R5 R2} should be asserted as I-L-Sets.
In a similar way, logical relations among point-based and interval-based elemental constraints can also be represented. For instance, the logical dependence "the duration of I1 is [5 8] if I2 is before I3 and the duration of I1 is [12 15] if I2 *is after I*3" can be represented as:
(I2 {b, bi} I3) ⇒ (I2
+{(0 ∞){Rb9} (-∞ 0]{Rb10}} I3
-), (I3
+{(0 ∞){Rb11} (-∞ 0]{Rb12}} I2
-),
{Rb10 Rb12} is an I-L-Set,
(I1
-{[5 8]{R1} [12 15]{R2}} I1
+),
and {R1 Rb11}, {R2 Rb9} are I-L-Sets, since Rb11 is associated to 'I2 *is after I*3' and Rb9 is associated to 'I2 *is before I*3'. Likewise, "I1 starts at the same time as I2 if t1 *occurs after t*2" can be represented as *(see Table 1)*:
I1 {s, ¬s} I2 ⇒ (I1
-{[0 0]{Rs1} (0 ∞){Rs3} (-∞ 0){Rs4}} I2
-) , (I1
+{(0 ∞){Rs2} (-∞ 0]{Rs5}} I2
+) ,
(t1 {(-∞ -1]{R1}, [0 0]{R2}, [1 ∞){R3}} t2),
and {R3 Rs3}, {R3 Rs4}, and {R3 Rs5} are I-L-Sets, since R3 is associated to 't1 *occurs after t*2' and Rs3, Rs4 and Rs5 are associated to 'I1 *does not start at the same time as I*2'.

## 6.1 Disjunctions Of Point And Interval-Based Constraints

Disjunctions of constraints between different pairs of points and intervals can be represented in the proposed model by means of labeled constraints between points and a set of I-L-Sets. This subsumes the related expressiveness in the subset of disjunctive linear constraints proposed by Stergiou and Koubarakis (1998), where only disjunctions of constraints between different pairs of points are managed.

To represent a *disjunctive set of disjunctive constraints between points*, we have 5:
(ni lcij nj) ∨ (nk lckl nl) *can be represented as:* (ni {lcij ∨¬lcij} nj) ∧ (nk {lckl ∨¬lckl} nl),
and some logical relation among lcij, ¬lcij, lckl and ¬lckl. Thus, the *disjunctive set* of constraints:
{(ni lcij nj) ∨ (nk lckl nl)} ≡ 
{(ni {(lecij.1){Rij.1}, (lecij.2){Rij.2}, ...., (lecij.p){Rij.p}} nj) ∨ 
(nk {(leckl.1){Rkl.1}, (leckl.2){Rkl.2}, ...., (leckj.q){Rkl.q}} nl)}