Scope ambiguities, monads and strengths

TL;DR

This paper compares three semantic scope assignment strategies—traditional movement, polyadic, and continuation-based—using monad concepts to analyze their computational properties and relationships, especially in handling scope ambiguities.

Contribution

It relates three scope strategies to monad structures, highlighting the role of monad constructs in understanding their differences and similarities.

Findings

Polyadic and continuation approaches heavily utilize monad constructs.

Traditional movement strategy does not explicitly use monad constructs but is related through them.

The paper clarifies how these strategies handle scope ambiguities in simple sentences.

Abstract

In this paper, we will discuss three semantically distinct scope assignment strategies: traditional movement strategy, polyadic approach, and continuation-based approach. As a generalized quantifier on a set X is an element of C(X), the value of continuation monad C on X, in all three approaches QPs are interpreted as C-computations. 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 wrt handling scopal ambiguities in simple sentences.