Underspecification and interpretive parallelism in Dependent Type Semantics

The scope parallelism in the Geach sentence (Every boy loves, and every girl detests, some saxophonist) and the related parallel interpretation requirement in pronominal binding is a pervasive phenomenon found across different types of coordination and ellipsis phenomena. Previous accounts all resort to additional constraints of some sort that restrict the otherwise flexible syntax-semantics interface to avoid overgeneration. In this paper, we propose a novel approach to this long-standing problem. We show that, by taking a proof-theoretic perspective on natural language semantics and by viewing the ambiguity resolution for pronouns and indefinites as underspecification resolution that invokes extra proof search, a conceptually natural solution emerges for the problem of interpretive parallelism. The analysis is cast in Dependent Type Semantics, with Hybrid Type-Logical Categorial Grammar as the syntax-semantics interface backbone. For empirical illustration, we show how the proposed approach correctly accounts for the classical Geach paradigm and its pronominal variant.