Logic History

With the Prior Analytics, Aristotle is credited with the earliest study of formal logic, and his conception of it was the dominant form of Western logic until 19th century advances in mathematical logic. Kant stated in the Critique of Pure Reason that Aristotle's theory of logic completely accounted for the core of deductive inference.

Aristotle "says that 'on the subject of reasoning' he 'had nothing else on an earlier date to speak of'".
However, Plato reports that syntax was devised before him, by Prodicus of Ceos, who was concerned by the correct use of words. Logic seems to have emerged from dialectics; the earlier philosophers made frequent use of concepts like reductio ad absurdum in their discussions, but never truly understood the logical implications. Even Plato had difficulties with logic; although he had a reasonable conception of a deducting system, he could never actually construct one and relied instead on his dialectic.
Plato believed that deduction would simply follow from premises, hence he focused on maintaining solid premises so that the conclusion would logically follow. Consequently, Plato realized that a method for obtaining conclusions would be most beneficial. He never succeeded in devising such a method, but his best attempt was published in his book Sophist, where he introduced his division method.