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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
which expresses the commutativity of addition, and
which expresses the infinitude of the primes.
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).
Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, 1958.
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