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

  exists y(x=2y),

which means that x is even (over the domain of integers), and

 x>1 ^  forall u forall v(x!=(u+2)(v+2)),

which means that x>1 and x is not the product of two numbers (both greater than one), i.e., x 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).

See also

Bound Variable, Closed Sentential Formula, Free Variable, Sentence, Sentential Formula

Portions of this entry contributed by Lew Baxter

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Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, 1958.

Referenced on Wolfram|Alpha

Open Sentential Formula

Cite this as:

Baxter, Lew and Weisstein, Eric W. "Open Sentential Formula." From MathWorld--A Wolfram Web Resource.

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