  Tarski introduces the notion of a sentential function. A sentential function S′ of a sentence S is the result of uniformly replacing the non-logical constants appearing in S with corresponding variables of suitable types (and different from the variables already existing in the language). For example, the sentential function determined by the sentence “∀x(Nx→¬Mx0)” is the expression “∀x(Px→¬Yxy)” (in which “P”, “Y” and “y” are new variables). It is equally possible to define the more general notion of a formula function, in an analogous way, except that now S may be an open formula. The sentential functions of sentences of LAr will not in general be sentences, and so will not always be either true or false by themselves. But they will always be either true or false with respect to interpretations of LAr; or, as Tarski says, they will be satisfied or not by interpretations of LAr.