This paper presents an approach to semantic interpretation for MTT that accounts for ambiguities of quantifier scoping. Dependency Tree Semantics (DTS) is described as a target formalism that introduces in the SemS a mechanism for dealing with quantifiers. DTS is based on underspecification, i.e. all ambiguous interpretations of a quantified sentence are represented in a single structure, where the scope relations are not given. The underspecified representations can be extended by adding dependency arcs that express the scope ordering when enough information is available for the disambiguation. Since a single underspecified structure covers all readings of a sentence, the mapping from the SSyntS to the SemS is heavily simplified. In order to provide some evidence about this, the paper includes the definition of the syntax-semantics mapping for a small fragment of English.
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