The form or logical form of an argument is the representation of its sentences using the formal grammar and symbolism of a logical system to display its similarity with all other arguments of the same type.
It consists of stripping out all spurious grammatical features from the sentence (such as gender, and passive forms), and replacing all the expressions specific to the subject matter of the argument by schematic variables. Thus, for example, the expression 'all A's are B's' shows the logical form which is common to the sentences 'all men are mortals', 'all cats are carnivores', 'all Greeks are philosophers' and so on.
That the concept of form is fundamental to logic was already recognized in ancient times. Aristotle was probably the first to employ variable letters to represent valid inferences (in the Prior analytics). (For which reason Łukasiewicz says that the introduction of variables was 'one of Aristotle's greatest inventions').
According to the followers of Aristotle (such as Ammonius), only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete terms man, mortal &c are analogous to the substitution values of the schematic placeholders 'A', 'B', 'C', which were called the 'matter' (Greek hyle, Latin materia) of the argument.