(1) A notion developed in mathematical logic and used as part of the conceptual apparatus underlying formal semantics (notably, in Lambda calculus). A type-theoretic approach offers a mathematical perspective for the categorial syntax of natural language, using the notion of a hierarchy of types as a framework for semantic structure (as in Montague grammar). Basic (or primitive) types (e.g. ‘entity’, ‘truth value’, ‘state’) are distinguished from derived or complex types (e.g. functional types: an example is (a, b), i.e. all functions taking arguments in the a domain apply to values in the b domain). Types are used in several models of lexical representation (notably, ‘typed feature structures’) to refer to a superordinate category. The types are organized as a lattice framework, with the most general type represented at the top and inconsistency indicated at the bottom. Similarities in lattices specify compatibility between types. Subtypes inherit all the properties of all their supertypes: for example, in a typed feature structure hierarchy, the subtype sausages under the type food (sausages are a type of food’) means that sausages has all the properties specified by the type constraints on food, with some further properties of its own.

(2) In lexical study, a term used as part of a measure of lexical density. The type / token ratio is the ratio of the total number of different words (types) to the total number of words (tokens) in a sample of text.