Examples
For example, the statement "''d2'' follows the weekday ''d1''" can be seen as a truth function associating to each tuple (''d2'', ''d1'') the value ''true'' or ''false''. The extension of this truth function is, by convention, the set of all such tuples associated with the value ''true'', i.e. By examining this extension, we can conclude that "Tuesday follows the weekday Saturday" (for example) is false. Using set-builder notation, the extension of the ''n''-ary predicate can be written as :Relationship with characteristic function
If the values 0 and 1 in the range of a characteristic function are identified with the values false and true, respectivelymaking the characteristic function a predicate, then for all relations ''R'' and predicates the following two statements are equivalent: * is the characteristic function of ''R'' *''R'' is the extension ofSee also
* Extensional logic * Extensional set *References