Completeness and Computational Efficiency for Underspecified Representations ∗

Cooper (1983) pioneered underspecified scope representation in formal and computational semantics through his introduction of quantifier storage into Montague semantics as an alternative to the syntactic operation of quantifying-in. In this paper we address an important issue in the development of an adequate formal theory of underspecified semantics. The tension between expressive power and computational tractability poses an acute problem for any such theory. Ebert (2005) shows that any reasonable current treatment of underspecified semantic representation either suffers from expressive incompleteness or produces a combinatorial explosion that is equivalent to generating the full set of possible scope readings in the course of disambiguation. In previous work we have presented an account of underspecified scope representations within Property Theory with Curry Typing (PTCT), an intensional first-order theory for natural language semantics. Here we show how filters applied to the underspecified-scope terms of PTCT permit both expressive completeness and the reduction of computational complexity in a significant class of non-worst case scenarios.