We adapt the notation of lambda abstraction to provide a way of linking the places of a predicate to blanks in an English sentence. An expression formed using our notation—which will have the general form [… x₁ … x_n …]_{x1 … xn}—is an abstract (in this use, a predicate abstract); it consists of a abstractor applied to a parenthesized body. In English notation, a predicate abstract takes the form what … x₁… x_n … says of x₁ … x_n. Variables in the body of an abstract are bound to the abstractor. (Variables in an abstractor that bind nothing in the body are cases of vacuous abstraction.)

Expressions that establish the same patterns of binding using different variables are alphabetic variants. They may be thought of as pronouns whose antecedents are in the abstractor. An expression (such as the body of an abstract) that has variables not bound to any abstractor, is not a sentence in the strict sense, but it does count as a formula. Formulas have many of the syntactic properties of sentences; in particular, they can be built from other formulas using connectives. And we can distinguish as atomic formulas not only unanalyzed sentences but all formulas that are predictions. (Indeed, unanalyzed sentences can be thought of as predications of zero-place predicates.)

Many pronouns in English function like the bound variables of the symbolic notation for abstracts, and abstracts can be used to represent the contribution of such pronouns to logical form.

Pronouns who antecedents are individual terms can be replaced by their antecedents. The corresponding process for abstracts is reduction. The opposite process, in which we restate sentences by introducing abstracts and bound variables is expansion.