Friday, June 24, 2011
When P must repeat a move
In his previous post, Jesse said that we'd speculated that the heuristic where P never repeats a move could be added to either D or E without any consequence (other than cutting down the search space). We'd thought this for quite some time but yesterday afternoon found various counterexamples, of which the simplest is the double negation of excluded middle: Here, P is required to repeat his attack on the negation in order for force P to attack the disjunction, so that he can go back and redefend it. (In a sense, this mimics the behavior you get when you drop D12, and allow repeat defenses to be. It's just that in this case, by allowing P to repeat his attack, he doesn't repeat his defense, because the defenses are to separate attacks.) But the pattern is more general: I'm pretty sure any double-negation of a classically-valid disjunction will require P to attack the same formula twice.