Scope ambiguities, monads and strengths

Continuation Semantics for Multi-Quantifier Sentences: Operation-Based Approaches

“…Here we only recall the definitions of the continuation monad, strengths and derived operations. For more details, we refer the reader to [20].…”

“…Strategy C allows a uniform in situ analysis of quantifiers. However, it cannot be straightforwardly extended to account for sentences involving 3 QPs -as discussed in [4] and proved in [20], it only provides four out of six readings available for such sentences. Below we define Strategy D, a minimally augmented empirically adequate version of Strategy C.…”

“…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. They achieve this at a certain price though (including loss in simplicity/uniformity of the semantic operations used) -as summarized by the In this paper, we first briefly recall the definitions of the semantic operations used in strategies A, B and C, i.e., mos'es, pile ′ up'es, CPS'es (for the details, see [20]). We then discuss the three in situ strategies C, D and E, together with their relative merits and costs with respect to the desiderata introduced.…”

“…Continuation-Based In Situ StrategiesBelow we illustrate Strategy C, D & E on examples involving one, two and three QPs (for the description of Strategies A & B, see[20]). In each strategy, the leaves in the Computation Trees have the same labels: QPs are interpreted as C-computations, and predicates are interpreted as lifted ('continuized') relations.…”