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pm k = pm i ∨ pm k = pm j iff op temp = Ch
T ( pm k )=( deb ( pm k ) , end ( pm k )) iff op temp = In
It ( n, pm i )=( ... (( pm i Sq pm i ) S q pm i ) ...Sq pm i )
n times
The temporal binary operator iter is defined by using the sequential operator Seq :
∀pme i ∈ PME, n∈ N
iter ( n, pme i )=( ... (( pme i Seq pme i ) S eq pme i ) ...Seq pme i )
n times
The sequential operator Seq is defined via the temporal relation T
as follows:
∀pme i , pme j ∈ PME× PME with T ( pme i )=( deb ( pme i ) , end ( pme i )) ,
T ( pme j )=( deb ( pme j ) , end ( pme j )) and end ( pme i )= deb ( pme j )
∃pme k ∈ PME such as pme k = pme i Seq pme j
and T ( pme k )=( deb ( pme i ) , end ( pme j ))
The choice operator is defined as follows:
∀pme i , pme j ∈ PME× PME ∃pme k ∈ PME such as
pme k = pme i choice pme j = ⇒ pme k = pme i ∨ pme k = pme j
4.5.3. Case study
To illustrate the formal model described above, we use an interaction scenario in
output inspired by the SmartKom system [REI 03]. It is a system for the management
of different applications relative to communication services (telephone, fax, email,
etc.) of access to diffuse computing devices, localization services and navigation
and road information. SmartKom is a symmetrical multimodal system whose output
multimodality is supported by the conversational agent Smartakus, which has an
inventory of gestures, postures and facial expressions.
The scenario of output multimodal interaction modeled consists of a dialog
between Smartakus and the user, who is asking for a map of the town of Heidelberg.
The conversational agent Smartakus responds to the user request by vocal synthesis:
Here you can see the map of the city ” while displaying the map of the town of
Heidelberg.
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