Logic is the principle of reasoned thinking.
History and specifics
The Vulcan people adopted logic as a way of life and, deeming emotions illogical, suppressed theirs. The Vulcans of the lost colony of the Last-of-all-Cities left the planet Vulcan before the spread of logic among their people and when they were rediscovered were disgusted by what had become of their civilization. They planned to hijack the USS Enterprise and return to Vulcan as conquerors. Spock could not understand this, noting how illogical their violence was given they had the capacity to construct an impulse engine themselves. (EV - Cloak and Dagger comics: "Cloak & Dagger", "Cloak and Dagger, Part 2")
The Vulcan understanding of logic underwent many phases in its history. In the 22nd century, the variation of logic practiced by many Vulcans involved considerably less emotional discipline than was often found in later practitioners. This was a result of the numerous interpretations of inaccurate recordings of Surak's teachings. The Syrrannites' particular take on logic was unpopular until the discovery of the Kir'Shara in 2154 by United Earth Starfleet Captain Jonathan Archer. With the discovery of the Kir'Shara, Surak's original set of teachings was revolutionized, and the tenants of Syrannitism came to dominate modern logic. (ENT episodes: "The Forge", "Awakening", "Kir'Shara")