An interpretation of a formula F in first-order logic is a nonempty domain D and an assignment of values to each constant, function, and predicate as follows:

1. To each constant, assign an element of D.
2. To each n-place function, assign a mapping:
   Dⁿ &rarr D.
3. To each n-place predicate, assign a mapping:
   Dⁿ &rarr {true, false}.

A formula &forall x G evaluates to true iff G is true for every x in D. A formula &exist x G evaluates to true iff G is true for some x in D. However, since most domains D are potentially infinite, evaluation by checking all values in D is generally not possible.

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