Open Sentential Formula
A sentential formula that contains at least one free variable (Carnap 1958, p. 24). A sentential variable containing no free variables (i.e., all variables are bound) is called a closed sentential formula. Examples of open sentential formulas include
 |
which means that 
is even (over the domain of integers),
and
 |
which means that 
and 
is not the product
of two numbers (both greater than one), i.e., 
is prime.
Closed sentential formulas are known as sentences, although it sometimes also happens that open sentential formulas are admitted as sentences (Carnap 1958, p. 25).
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