Fig. 1, treble clef. "A syllogism's letters can be best represented in music— take E, for example." -Marilyn Damord The letters A, E, I, and O have been used since the medieval Schools to form mnemonic names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE, etc. Next to each premise and conclusion is a shorthand description of the sentence. So in AAI-3, the premise "All squares are rectangles" becomes "MaP"; the symbols mean that the first term ("square") is the middle term, the second term ("rectangle") is the predicate of the conclusion, and the relationship between the two terms is labeled "a" (All M are P). The following table shows all syllogisms that are essentially different. The similar syllogisms share the same premises, just written in a different way. For example "Some pets are kittens" (SiM in Darii) could also be written as "Some kittens are pets" (MiS in Datisi). In the Venn diagrams, the black areas indicate no elements, and the red areas indicate at least one element. In the predicate logic expressions, a horizontal bar over an expression means to negate ("logical not") the result of that expression. It is also possible to use graphs (consisting of vertices and edges) to evaluate syllogisms. Examples Barbara (AAA-1) Celarent (EAE-1) Similar: Cesare (EAE-2) Darii (AII-1) Similar: Datisi (AII-3) Ferio (EIO-1) Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4) Baroco (AOO-2) Bocardo (OAO-3) Barbari (AAI-1) Celaront (EAO-1) Similar: Cesaro (EAO-2) Camestros (AEO-2) Similar: Calemos (AEO-4) Felapton (EAO-3) Similar: Fesapo (EAO-4) Darapti (AAI-3) Table of all syllogisms This table shows all 24 valid syllogisms, represented by Venn diagrams. Columns indicate similarity, and are grouped by combinations of premises. Borders correspond to conclusions. Those with an existential assumption are dashed. Terms in syllogism With Aristotle, we may distinguish singular terms, such as Socrates, and general terms, such as Greeks. Aristotle further distinguished types (a) and (b): Such a predication is known as a distributive, as opposed to non-distributive as in Greeks are numerous. It is clear that Aristotle's syllogism works only for distributive predication, since we cannot reason All Greeks are animals, animals are numerous, therefore all Greeks are numerous. In Aristotle's view singular terms were of type (a), and general terms of type (b). Thus, Men can be predicated of Socrates but Socrates cannot be predicated of anything. Therefore, for a term to be interchangeable—to be either in the