A Logic Error (ロジックエラー Rojikku Erā ) is the worst mistake that a Game Master can make. A Logic Error occurs when there is a contradiction in the tale that the Game Master created. The only Logic Error seen thus far was caused by Battler and Erika in Battler's game Dawn of the Golden Witch. When a Logic Error is made, the Game Master can either fix it or admit their mistake. If they admit their mistake the game board is immediately destroyed. However, if a Game Master does not give up then they have an eternity to fix the error. Due to the fact Logic Errors are far from easy to fix, this is viewed as being an eternal torture.
Both Bernkastel and Lambdadelta have gone through this torture. This is the true reason that they avoid boredom. If they get bored then they will remember the torture that they were put through so they play games and keep themselves entertained to forget about their past. Bernkastel's case specifically demonstrates that Logic Errors can be forced on a piece by a Game Master. Bernkastel, when she existed as a piece, was given the responsibility of solving the Logic Error without even knowing it. She managed to do so and became the Witch of Miracles.
Battler's error was an imprisonment in a closed room. He wanted to make his game board corpse disappear and could trick Erika a short time. His final step was to rescue his unconfirmed corpse by another victim of the crime. The survivors of the first twilight have been sealed away in a so-called closed room.
The death of the victims wasn't confirmed by Erika but she made sure that they all were dead by beheading the bodies and dropping the heads close to the corpses. That way nobody could rescue Battler of his closed room and reattach the chain after his suspected body left the room.
Erika's Logical Error is an interpreted one. Introduced by the reborn Beatrice after Battler went to hell.
Battler understood the truth about Beatrice in the 5th game. Erika only concluded possibilities. She didn't know that Kanon and Shannon are Beatrice therefore 1 human. Meaning locking up the survivors in 2 closed rooms is impossible because they can't coexist with presence of people who don't know the truth. That destroyed those closed rooms.
It can be implied that Battler planned such a thing from the start to revive the Beatrice he knew, because if he reached the truth in the 5th Game, there is no way that he could have been trapped by this Logic Error.