The proposed reasoning processes can manage *context-dependent* disjunctive constraints in a way similar to previously defined labeled disjunctive constraints (Section 3). For instance, according to the constraints and contexts in Figure 13, the following input labeled constraints between nodes n1 n2 should be updated:

$$\langle\mathbf{u}\rangle=\mathbf{u}\cdot\mathbf{u}$$

(n1 {[0 100]{R1 W0}, [200 300]{R2 W0}} n2), (n1 {[0 50]{R3 W1}, [200 210]{R4 W1}} n2),

(n${}_{1}$ {[60 100]${}_{\{\rm RS\,w2\}}$, [290 300]${}_{\{\rm R6\,w2\}}$} n${}_{2}$), (n${}_{1}$ {[0 25]${}_{\{\rm R0\,w11\}}$} n${}_{2}$), (n${}_{1}$ {[0 20]${}_{\{\rm R0\,w31\}}$, [210 215]${}_{\{\rm R0\,w32\}}$} n${}_{2}$),
(n1 {[60 100]{R5 W2}, [290 300]{R6 W2}} n2), (n1 {[0 25]{R7 W3}, [260 280]{R8 W3}} n2),
(n1 {[0 20]{R0 W31}, [210 215]{R0 W32}} n2), (n1 {[260 280]{R0 W33}} n2).
$=\;\;\text{Two}\,\!\uparrow\,\!\uparrow$  . 
$\mathbf{a}$
(n1 { [0 25]{R0 W11}} n2), (n1 { [30 50]{R9 W12}, [200 205]{R10 W12}} n2),
$$\tau_{l}\;\mathbf{J}$$
(n${}_{1}$ {[0 25]${}_{\{\rm R7\,w3\}}$, [260 280]${}_{\{\rm R8\,w3\}}$} n${}_{2}$), (n${}_{1}$ {[30 50]${}_{\{\rm R9\,w12\}}$, [200 205]${}_{\{\rm R10\,w12\}}$} n${}_{2}$), (n${}_{1}$ {[260 280]${}_{\{\rm R0\,w33\}}$} n${}_{2}$).  

![0_image_0.png](0_image_0.png)

$$\mathbf{O}_{1}\{\mathbb{R}3\ \mathrm{W1}\},\ [2000]$$

The updating process of each new constraint cij in a given context Wp should assure the consistency of cij in the context Wp, as well as in its predecessor contexts(Figure 13). The consistency of cij with the successor contexts of Wp will be detailed in Section 7.2, since several options can be identified. However, it is not necessary to assure consistency among constraints belonging to contexts of different hierarchies. Successor contexts of a given context represent different alternatives, which are mutually exclusive. Thus, constraints belonging to contexts of different hierarchies can be mutually inconsistent. However, this does not imply that constraints in these contexts should necessarily be mutually disjoint. For instance (Figure 13), the constraints (n1 {[0 50]{R3 W1}, [200 210]{R4 W1}} n2) in context W1 and (n1 {[0 25]{R7 W3}, [260 280]{R8 W3}} n2) in context W3 are not mutually disjoint. However, W1, W2 and W3 are assumed as three mutually exclusive alternatives of W0.