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The classic example:

All whales are animals that breathe by means of lungs.<br> All whales are mammals.<br> All whales are animals that breath by means of lungs.<br>

In the Prior Analytics, Aristotle presents the first system of logic, the theory of the syllogism (see the entry on Aristotle's logic and ch. 1 of Lagerlund 2000 for further details). A syllogism is a deduction consisting of three sentences: two premises and a conclusion. Syllogistic sentences are categorical sentences involving a subject and a predicate connected by a copula (verb). These are in turn divided into four different classes: universal affirmative (A), particular affirmative (I), universal negative (E) and particular negative (O), written by Aristotle as follows:

A – A belongs to all B (AaB) I – A belongs to some B (AiB) E – A does not belong to any B (AeB) O – A does not belong to some B (AoB)