Scope ambiguities, monads and strengths

In this paper, we will discuss three semantically distinct scope assignment strategies: traditional movement strategy, polyadic approach, and continuation-based approach. Since generalized quantifiers on a set X are elements of C(X), which is the value of the continuation monad C on X, quantifier phrases are interpreted as C-computations, in all three approaches. The main goal of this paper is to relate the three strategies to the computational machinery connected to the monad C (strength and derived operations). As will be shown, both the polyadic approach and the continuation-based approach make heavy use of monad constructs. In the traditional movement strategy, monad constructs are not used but we still need them to explain how the three strategies are related and what can be expected of them with regard to handling scopal ambiguities in simple sentences.