Below is from reference here:
To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences in the original argument.
All humans are mortal.
Socrates is human.
Therefore, Socrates is mortal.
All H are M.
S is H.
Therefore, S is M.
All that has been done in the argument form is to put H for human and humans, M for mortal, and S for Socrates. What results is the form of the original argument. Moreover, each individual sentence of the argument form is the sentence form of its respective sentence in the original argument.
Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.
So clearly logical forms are not unique and can be expressed in different ways such as propositional or more formal predicative first order fashions, but the key thing is it has to preserve its original semantic meaning from natural language. The idea is that once you arrive at a correct formal logical form, it should be fairly easy and nearly automatic to determine its formal validity (such as using proof checker programs). You may regard its corresponding formal system's inference rules as the more syntactic part to complete the above evaluation.