The Limitation of Propositional Logic

Discrete Mathematics: The Limitation of Propositional Logic
Topics discussed:
1) Limitation of Propositional Logic.
2) The need for First-Order Logic or Predicate Logic to overcome the limitation of Propositional Logic.
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Predicates
A predicate is a boolean function whose value may be true or false,
depending on the arguments to the predicate.
* Predicates are a generalization of propositional variables.
* A propositional variable is a predicate with no arguments.
Example - Consider the following boolean propositions:
A (Adam is tall)
B (Beth is tall)
C (Carl is tall)
:
Z (Zeke is tall)
We need a different proposition for each person; each of these propositions
is either true or false.
We can capture the same set of truth values using a single predicate (or
boolean function), Tall(x).
Tall(x) is true whenever person x is tall, and is false otherwise.
* Tall(Adam) is true if proposition A above is true.
* Tall(Beth) is true if proposition B above is true.
* Tall(Carl) is true if proposition C above is true.
(www.cs.rochester.edu/u/scott/courses/173/notes/09_pred_logic#:~:text=One%20key%20limitation%20is%20that,what%20predicate%20logic%20is%20for.)