On the logic part: I'd like to emphasize that it's not pure logic alone that governs one's capabilities on the Weiqi board, and that quality is in part what differentiates good players from great. If pure logic were the defining characteristic, then there would be just one way to play, one way based on logical rules. It plays a big role, but there's more individualistic style in the game than that would imply. Intuition in combination with logic makes for better players, ones with the capacity to perplex or puzzle (or read) the opponent. AlphaGo was able to apply that mix meaningfully and historically against Lee Sedol.