Continuation semantics for multi-quantifier sentences: operation-based approaches

Classical scope-assignment strategies for multi-quantifier sentences involve quantifier phrase (QP)-movement. More recent continuation-based approaches provide a compelling alternative, for they interpret QP's in situ - without resorting to Logical Forms or any structures beyond the overt syntax. The continuation-based strategies can be divided into two groups: those that locate the source of scope-ambiguity in the rules of semantic composition and those that attribute it to the lexical entries for the quantifier words. In this paper, we focus on the former operation-based approaches and the nature of the semantic operations involved. More specifically, we discuss three such possible operation-based strategies for multi-quantifier sentences, together with their relative merits and costs.