A formal language was invented by Aristotle and used by him in his lectures. This formal language consisted of Greek capital letters used as placeholders, arrayed in the schemata of the three figures recognized as authentically Aristotle’s. In these arrays, arcs under the placeholder letters indicate how the terms are linked in the premisses and conclusion and are read as some inflection of ΰπάρχειν, used by Aristotle as a second- order expression to convey the relation that the terms—not the designata of the terms-of a syllogism have to one another. It is further possible that Aristotle elaborated the three- term arrays with arcs into lime and triangle diagrams like those appearing in Ammonius, Philoponus and the Scholia Platónica. The lune and triangle diagrams are developed easily out of the three-term arrays with arcs, and they are consistent with the figures’ being the schemata of their instances the moods, which moods are in turn schemata of the syllogisms themselves. Conditions in Aristotle’s classroom make it plausible that the diagrams were in use there, whether by master or by pupil. These diagrams serve as proof forms, as does the pons asinorum diagram, obviously constructible from Aristotle’s remarks in Prior Analytics 1: 27-28. As proof-forms of the syllogistic, the diagrams are not mere addenda to Aristotle’s system, which makes it more likely that he developed them himself.
This formal language in the Prior Analytics accommodates all the kinds of propositions that are discussed in the Categories, On Interpretation, and Topics. The analysis of Aristotle’s formal language presented here corrects the views that his logic uses propositions of the subject-copula-predicate form and that the intended interpretation of his syllogistic is as a logic of class inclusion and exclusion.
Mulhern, Mary, "Aristotle's Formal Language" (2005). The Society for Ancient Greek Philosophy Newsletter. 398.