Let me know when you can prove that "logical" and "intelligent" were ever stored on the same shelf, much less being meaningfully equivalent. If anything, we know that making a general intelligence (the only natural example of it we know) emulate logic is crazily inefficient and susceptive to biases that are entirely non-existent (save for bugs) in much simpler (and energy-efficient) implementations of said logic.

An AGI that can't even play a game of chess, a game that children learn to play, without making an invalid move doesn't really sound like an AGI.