Scope (formal semantics)

Others theories compute scope relations in the semantics itself, using formal tools such as type shifters, monads, and continuations.

However, this generalization seems to be contradicted by Haddock descriptions such as the following: This noun phrase is felicitous to use in this context, even though there is no unique hat.

What seems to license this surprising use of the definite description is the fact that the context contains a unique rabbit-containing hat.

To cash out this idea, it has been proposed that the uniqueness presupposition of "the hat" takes scope separately from the rest of the definite's meaning.

In other words, a witness set is established low in the structure, but is checked for singletonness higher up.

For instance, as illustrated by Sentence 1 below, quantifiers that originate inside an if-clause usually cannot take scope outside of that "if"-clause.

Examples of this sort have been used to argue that scope relations are determined by syntactic movement operations.

[13] Recent work such as Charlow (2020) treats indefinites as denoting sets of individuals which can be type shifted so that they take scope in a manner similar to Karttunen's (1977) alternative-based mechanism for wh-questions.

[16] In structural approaches, discrepancies between an expression's surface position and its semantic scope are explained by syntactic movement operations such as quantifier raising.

Since type shifters are applied during the process of semantic interpretation, this approach allows scopal relations to be partly independent of syntactic structure.