Can you convert a categorical proposition into a zeroth order proposition?

Question

I am a student learning mathematical logic as a hobby. When I say "zeroth order" I mean "not predicate logic".

Question: Is it possible to convert a categorical proposition into a zeroth-order proposition?

For example: If I have a categorical proposition "All $S$ are $P$", then can I construct an implication that says "If an object is $S$, then the object is $P$"?

If this is possible, then is there a specific replacement rule for accomplishing this? Does the replacement depend on whether the categorical proposition is $A$, $E$, $I$, or $O$?

Answer 1

"All $S$ are $P$" is translated in modern logic exactly as "For every $x$, if $x$ is $S$ then $x$ is $P$", i.e. as $∀x(Sx → Px)$.

Categorical propositions are part of the theory of Syllogism. In modern terms, it is part of an interesting fragment of predicate logic: the so called monadic predicate calculus.

But regarding the title question, the answer is: no.

In propositional logic we can have $S → P$ and $S ∧ P$, but we cannot express the difference between "all" and "some".