Propositional Logic has several limitations. One key limitation is that it applies only to atomic propositions. There is no way to talk about properties that apply to categories of objects, or about relationships between those properties. That's what predicate logic is for. Predicate logic is a mathematical model for reasoning with predicates: functions that map variables to truth values. As in propositional logic, we can create logical expressions containing predicates, manipulate those expressions according to the algebraic laws of predicate logic, and construct proofs using rules of inference to deduce new facts from axioms. In fact, proofs in predicate logic (based on unification) are a form of computation used in the programming language Prolog. Although predicate logic is more powerful than propositional logic, it too has its limits.
Comparison and Limitation of Propositional logic and Predicate Logic