Examples of the classification of words by semantic types.

The primitive types are entities e, exemplified by proper nouns such as Darwin (Class 1), and truth values, t (which are the values of sentences). Predicates or relations, such as the simple verb die, and the adjective/noun blue, take entities as arguments and map them to sentences (e.g., Darwin dies, Tahoe is blue). They are classified as (Class 2). The notation denotes a mapping from an element in the domain to the image [43], [44]. The semantic types of higher Classes are established by assessing what mappings they perform when they are instantiated. For example, everyone is of type (Class 3), because it is a mapping from sets of properties of entities to truth values [44]; the verb believe shares this classification as a verb involving mental representation. The adverb supposedly is a higher order operator (Class 4), because it modifies other modifiers. Following Ref. [44] (contra Ref. [43]) words are coded by the lowest type in which they commonly occur (see Text S1, Coding of Semantic Types).