- Sentence (mathematical logic)
:"This article is a technical mathematical article in the area of predicate logic. For the ordinary English language meaning see

Sentence , for a less technical introductory article seeStatement (logic) ."In

mathematical logic , a**sentence**of apredicate logic is awell formed formula with nofree variable s. A sentence is viewed by some as expressing aproposition . It makes an assertion, potentially concerning any structure of "L". This assertion has a fixedtruth value with respect to the structure. In contrast, the truth value of a formula (with free variables) may be indeterminate with respect to any structure. As the free variables of a formula can range over several values (which could be members of a universe, relations or functions), its truth value may vary.**Example**The following example is in

first-order logic .:$forall\; yexists\; x\; (x^2=y)$

"is" a sentence. This sentence is true in the positive

real numbers but false in the real numbers. (In plain English, this sentence is interpreted to mean that every member of the structure concerned is the square of a member of that particular structure.) On the other hand, the formula:$exists\; x(x^2=y)$

is "not" a sentence, because of the presence of the free variable "y". In the structure of the real numbers, this formula is true if we substitute "y" = 2, but is false if "y" = –2.

**ee also***

Ground expression

*Atomic sentence

*Open sentence

*Statement (logic)

*Proposition **References**

*Wikimedia Foundation.
2010.*

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