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Closed Sentential Formula

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

forall x forall y(x+y=y+x),

which expresses the commutativity of addition, and

forall x exists y( forall u forall v(x+y!=(u+2)(v+2))),

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).

See also

Bound Variable, Free Variable, Open Sentential Formula, Sentential Formula

Portions of this entry contributed by Lew Baxter

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References

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

Referenced on Wolfram|Alpha

Closed Sentential Formula

Cite this as:

Baxter, Lew and Weisstein, Eric W. "Closed Sentential Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ClosedSententialFormula.html

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