# Assignment

**Assignment** refers to the function which assigns a reference to a variable. The truth-value of quantified formulas is determined with respect to a given assignment.

### Example

In order to determine whether All*(v)*[P] is true with respect to an assignment *g* we have to check whether P is true for every assignment *g** differing at most from *g* in the value it assigns to v. Exists*(v)*[P] is true with respect to an assignment g when P is true for at least one assignment *g** which may only differ from *g* in the value it assigns to *v*.

### Comment

The use of assignments to variables makes it possible to interpret multiply quantified formulas in a compositional way.

### Link

Utrecht Lexicon of Linguistics

### References

Gamut, L.T.F. 1991. *Logic, language, and meaning.* Chicago: Univ. of Chicago Press.