Quantifiers in Dependency Tree Semantics

Dependency Tree Semantics (DTS) is an underspecified formalism for represent-ing quantifier scope ambiguities in natural language. DTS features a direct inter-face with a Dependency grammar and an incremental, constraint-based disam-biguation mechanism. This paper focuses on the meaning of quantifier depend-ency in DTS: we show how well formed structures can be translated into formu-lae of a Second Order Logic augmented with Mostowskian generalized quantifi-ers. Of particular intererest is the natural way that branching quantification is rep-resented in DTS. We generalize existing work in this area to obtain a theory of the meaning of branching quantification that is of interest independent of DTS as well.