Okay, let me see if I understand your example.
We have a program that calculates numbers. This program also has a function in it that will disable a means of calculation if activated. Now, from my experiance with Java, there is no way to disable math the way we use it. Now, we could make a program where you could enter your numbers, and "tell" it to add, and the program would then do something entirely different, but it would still be using logic, as the program would have been designed to do so. Like for example, we enter in 3 and 4, and tell the computer to add them, but instead, the program is programmed to subtract them and multiple by 2, it would appear that the program is doing it wrong, but the program is being completely logical with what its programmed to do. But its not like the computer just stopped using logic.
I don't think thats a very good example with someone blacking out or forgetting something. There its not like you would wake up, and start randomly attacking people, you would just be confused about whats going on. I wouldn't call that illogical. I would say that would be ignorance, but that is different from what we're talking about here.
In the murder example, the guy would have just stopped using logic. Instincts are not logical. You might say, "Well, they were logical to him, but no to us." Well, in that example, he didn't even think about what he was doing, he was not applying his own personal logic system to it. It was instinct.
I feel like I'm rambling, and can't get my point across very well...