Scope (formal semantics)

In formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "Paulina doesn't drink beer but she does drink wine," the proposition that Paulina drinks beer occurs within the scope of negation, but the proposition that Paulina drinks wine does not. Scope can be thought of as the semantic order of operations. One of the major concerns of research in formal semantics is the relationship between operators' syntactic positions and their semantic scope. This relationship is not transparent, since the scope of an operator need not directly correspond to its surface position and a single surface form can be semantically ambiguous between different scope construals. Some theories of scope posit a level of syntactic structure called logical form, in which an item's syntactic position corresponds to its semantic scope. Others theories compute scope relations in the semantics itself, using formal tools such as type shifters, monads, and continuations. The scope of an operator need not correspond directly to the word order of the sentence it occurs in. For instance, some sentences display a scope ambiguity in that the relative scopes of two operators can be construed in multiple ways. Every hedgehog is friends with a giraffe. This sentence can be understood in two ways. On the inverse scope reading, there is a single giraffe who is very popular in the hedgehog community. On the surface scope reading, the sentence can be true even if the hedgehogs are friends with different giraffes. Split scope is the phenomenon where different components of an expressions item's meaning take scope in different places. Negative quantifiers are one category of expression which have been argued to take split scope. The company need fire no employees. On the de re (non-split) reading, this sentence means that there is no employee such that the company needs to fire that employee. This is a non-split scope reading since "no" simply takes scope above the modal "need".