A
propositional function in
logic, is a sentence expressed in a way that would assume the value of
true or
false, except that within the sentence is a
variable (
x) that is not defined or specified, which leaves the statement undetermined. Of course, the sentence can consist of several such variables (e.g.
n variables, in which case the function takes
n arguments). As a
mathematical function,
A(
x) or
A(
x1,
x2, · · ·,
x), the propositional function is abstracted from
predicates or propositional forms. As an example, let's imagine the predicate, "x is hot". The substitution of any entity for
x will produce a specific proposition that can be described as either true or false, even though "
x is hot" on its own has no value as either a true or false statement. However, when you assign
x a value, such as
lava, the function then has the value
true; while if you assign
x a value like
ice, the function then has the value
false.