MTT and the quantifier scope ambiguity

Sentences with more than one quantifier can have different interpretations depending on the scope order of their quantifiers. To our knowledge, this type of ambiguity has received a lot of attention in the Underspecification literature but not in the MTT one. In this paper, we define a new underspecified SemS of MTT which refers to all possible readings of a sentence. In order to specify a particular scope order, we introduce additional dependencies. They roughly correspond, in FOL, to Skolem constants and functions and are part of a new additional structure of SemR level, named SemCtxDepS.