Third, in the VP′-rule, variables x and y are assumed to be of type e (they take basic individuals as values), and the denotation of a transitive verb should be thought of as a function that is applied first to the object, and then to the subject (yielding a function from worlds to truth values—a sentence intension). The lambda-abstractions in the VP′-rule can be understood as ensuring that the object NP, which like any NP denotes a second-order property, is correctly applied to an ordinary property (that of being the love-object of a certain x), and the result is a predicate with respect to the (still open) subject position. The following is an interpreted sample vocabulary: