A closed sentential formula is a sentential formula in which none of the variables are free (i.e., all
variables are bound). Examples of closed sentential
formulas are given by

A closed sentential formula is called a sentence (Carnap 1958, pp. 24-25 and 85). However, in some language systems, open
sentential formulas are also admitted as sentences (Carnap 1958, p. 25).