limbinding

Limbinding is a term used in some theories of formal semantics to describe a binding mechanism for limit expressions within the semantic structure of a sentence. It focuses on how cardinal or measure-based constraints (such as exactly, at most, or more than a certain number) attach to the entities they constrain and interact with other operators like negation, modals, or conditionals.

In a typical account, limbinding introduces a dedicated operator, often called LIM, that binds a variable over the domain of discourse or a subdomain relevant to a determiner phrase. The LIM operator imposes a numerical or quantitative bound on the set described by the restrictor of the determiner. Semantically, this allows the theory to distinguish the scope of the limit from other elements in the sentence, enabling predictions about when a limit is taken to be wide-scope or narrow-scope relative to the surrounding operators.

Examples illustrate the idea. For the sentence Exactly three students passed, limbinding captures that the quantity of students satisfying Pass(x) is precisely three, with the binding constrained to the relevant domain of students. In embedded constructions, such as If exactly three students passed, the LIM operation interacts with the conditional, potentially changing which parts of the sentence the limit applies to depending on the scope chosen by the theory.

Limbinding remains a topic of discussion within formal semantics. It is proposed as a tool to explain certain scope interactions of cardinal determiners, though it competes with alternative accounts grounded in standard cardinality semantics or dynamic/ handler-based approaches. See also: scope, determiners, cardinality, and dynamic semantics.