is the "value" of the function for the argument
. If
is a one-many relation, the range of possible arguments to the function is the converse domain of
, and the range of values is the domain. Thus the range of possible arguments to the function "the father of
" is all who have fathers, i.e. the converse domain of the relation father, while the range of possible values for the function is all fathers, i.e. the domain of the relation.
Many of the most important notions in the logic of relations are descriptive functions, for example: converse, domain, converse domain, field. Other examples will occur as we proceed.