Explore the quest for mechanically systematizing reasoning in propositional logic through this 28-minute video lecture. Delve into the historical context of this pursuit, from Aristotle and the Stoics to Leibniz and George Boole. Discover two powerful solutions to the Holy Grail of Propositional Logic using the Algebra of Boole: Boole Reduction and the Boole-Mobius transform. Follow along as the lecturer applies these methods to solve a logic problem involving Sir Galahad's search for the Holy Grail. Gain insights into the efficiency and recursive aspects of the Boole-Mobius transform, and understand how these approaches contribute to the advancement of propositional logic.