The forms of logical reasoning studied by Aristotle are called syllogisms. A contemporary description of them can be read in my paper included in the logical part of this Web-site. Generally speaking, any syllogism consists of 3 sentences: 2 premises and 1 conclusion. Each of them is of one of the following 4 types: every... is..., some... is..., no... is... and some... is not... where ellipses replace properties (or classes) called traditionally terms. The terms are 3 in number and each sentence contains two of them,  all three pairs being different. Combining all possible dispositions of 3 terms in 4 sentences, 256 syllogisms are obtained. Aristotle proved that 19 of them are true. They have been named so that the vowels and consonants indicate the interrelations between them. At one time when syllogistic was believed to be the whole lot of logic, the rote of the names took a central place in the scholastic education. As a result, an enigmatic and very esoteric system of rules has been developed converting logical proofs in a kind of exorcism. Here you are an ancient verse involving the 19 names of syllogisms divided into 4 groups called figures:

Barbara, Celarent, Darii, Ferio-que, prioris;
Cesare, Camestres, Festino, Baroco, secundae;
Tertia, Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison, habet;
Quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison.

Typus Logice (the "Picture of Logic") is a woodcut published in the 1517 edition of Gregor Reisch's Margarita philosophica, a popular textbook on mediaeval science. In fact, it is an encyclopaedia of the Seven Liberal Arts and Logica is one of them. Dame Logica is represented as a huntress chasing the hare Problema in the company of her retriever dogs Veritas and Falsitas. She is bravely  pacing bypassing the Sylua opinionum (the "forest of opinions"; the label does not appear in this version of the woodcut) as well as the covert of the Insolubilia ("insoluble problems"). The trees are named after four famous scholastic philosophers: Albertus Magnus, Duns Scotus, William Occam, and Thomas Aquinas. Some troubles can be met by her way: bushes Parua logicalia ("elementary logical matters") and stones Fallacie but she is striding them. The buxom huntress lustily blows her horn Sonus vox ("spoken word"), from which two Premisse in the shape of two roses emerge. Dame Logica's dress and equipment include the stomacher Conclusions, the bow Questio, the hunting-knufe Syllogismus, and the quiver Locus from which arrows Argumenta are pricking up. Even her boots have been named after logical notions: Predicamenta and Predicabilia. It is remarkable that Veritas, the nimble retriever, is almost caught up the hare, while Falsitas is lazy and standing idly by.

In the 1508 edition of Margarita philosophica, one can see the label Sylua opinionum, some other labels are relocated, etc. (Sorry for the bad reproduction!) However, there is an important element which had disappeared in later editions: the mountain summits behind the huntress. They have been marked with the 4 syllogistic terms: Omnia ("all"), Quidam ("some"), Nullus ("nobody"), and Quidam non ("some not"). The man contemplating those four summits is the ancient philosopher Parmenides who, according to the legend, spent his life on a rock in building a system of logic. Another remarkable difference: both dogs are equally energetic and this fact may be noted as a defect. However, taking in account the sharp ears and the hirsute brush of Falsitas, one may conclude that it is a wolf or a fox simulating Veritas. Indeed, that is the central function of the falsehood, isn't it?
 

It is surprising how complicated logical tools find their artistic embodiment. Even syllogisms have been personalized! The canvas by Paulus Bor (1600-1669) is entitled Allégorie du Syllogisme (Musée des beaux arts, Rouen). The image has been borrowed from the Web-site of Carlos Parada devoted to Greek mythology. A serpent is seen twined round the girl arm. Why it is just the reptile Bible has stigmatized as the most perfidious and maleficent for the mankind? The answer is given in the Bible again. The serpent is as perfidious as clever and sage: "Now the serpent was more subtle than any beast of the field which Jehovah God had made" (Genesis, 3:1); "Be ye therefore wise as serpents, and harmless as doves" (Matthew, 10:16). In addition, the artist might connected serpent's zigzag motions with the impression of syllogism as tacking between true and false conclusions.