 In the literature on many-valued logic it is sometimes proposed to consider a set of antidesignated values which not obligatorily constitute the complement of the set of designated values (see, e.g., Rescher 1969, Gottwald 2001). The set of antidesignated values can be regarded as representing a generalized concept of falsity. This distinction leaves room for values that are neither designated nor antidesignated and even for values that are both designated and antidesignated.