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not restrictive and in fact does not have anything to do with the referent
identification, for which “this itinerary” is necessary and sufficient. Finally,
let us mention the particular importance of the determiner: with “the green
pyramid”, the singular definite determiner is translated by a very specific
research criterion: find the unique green pyramid in a set of objects that
should contain pyramids and objects with other shapes, as well as the green
objects and the objects of other colors. The demonstrative determiner in “this
itinerary” has a completely different role: it shows that the referent is salient
in the communication situation, either because it has just been mentioned, in
which case this is an anaphora such as in “the itinerary which goes from Paris
to Meudon seems shorter” followed by “I will pick this one”, or because it is
simultaneously pointed at by a gesture, which is the case in utterance U2.
This fine determiner analysis will allow us to implement a performing object
reference resolution.
6.1.1. Multimodal reference domains
After one of Corblin's intuitions [COR 95] and a set of work carried out in
Nancy [LAN 04, p. 107], the notion of reference domain proved its
importance for reference resolution in a linguistic as well as multimodal
context [LAN 06]. The idea is that the identification of referents
systematically happens by identifying a contextual subset to which they
belong. This subset, which does not extend to the entirety of the context but
matches, for example, a focus space, is called a reference domain. It allows us
to justify the use of the singular definite determiner as in “the green pyramid”,
even in the cases when the context has more than one pyramid: if there is a
previously defined focus space drawn during the dialogue, and this focus
space has a single green pyramid, then chances are that the singular definite is
not a mistake on the user's part but a localized interpretation in the reference
domain, which is this specific focus space.
Compared to the discourse representation theory and its extension for
multimodal dialogue MDRT [PIN 00], the multimodal reference domain
model carries out a finer process of the focalization on a contextual subset.
Compared to the quantification domain approach (thanks to the work of R.
Montague), reference domains last more than one utterance and take into
account contextual restriction and broadening mechanisms as the dialogue
progresses from a referential point of view. We mention them here for
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