TITLE: What is the difference between a predicate and function?
QUESTION [21 upvotes]: I need to to understand the difference between predicates and functions in the context of Clasual Form Logic in order to define the Herbrand universe.
If I have p(x) :- q(f(x)) would I be right in saying that p and q are predicates while f is a function because it is "nested"?  By this thinking then if I have p(x) :- q(x) both p and q are predicates and I have no functions?
If this is incorrect then how can I tell the difference between a predicate and function?

REPLY [2 votes]: The terms "Function" and "Predicate" are only and solely determined by the formal system in which those words are being used/defined. In most formalizations of first order predicate logic the words "predicate" and "function" classify two different kinds of signs (the function signs and the predicate signs) each of which follow different rules of use i.e. function signs are different from predicate signs because the rules for using function signs are different from the rules for using predicate signs.