Korzybski took the notion of a propositional function from philosophy, particularly from Russell and Frege.
Simple propositions are generaly simple declarative sentences with a subject, the copula 'is' and a class or set name, such as "Fido is a dog." D(f) where D() is "dogness" and f is Fido. In this case D() is a function to truth values. If Fido is a dog then D(f)=T, but if Fido is not a dog, then D(f)=F.
Propositional functions express a more general structure where the subject is a variable, but the value is not a truth value, but a proposition simpliciter. In the above example, let D'() stand for the propositional function.
Then the value of D'(f) is the simple proposition: "Fido is a dog."
The property function maps individuals to truth values.
The propositional function maps individuals to propositions.
quote:... a propositional function is a function from individuals to propositions (1973: 209).
Thomason, Richmond H. & Stalnaker, Robert C., 1973. “A Semantic Theory of Adverbs,” Linguistic Inquiry 4: 195-220.
Proposition: Fido is a dog.
Let D be the set of dogs, cats, mice, and anything else you want to add.
Let the set of propositions include:
Micky is a mouse.
Fido is a cat.
Dumbo is an elephant.
Fido is a dog.
A propositional function would map Fido to "Fido is a dog.".
PF:Fido -> "Fido is a dog."