It may not be clear what you meant by “length” of contradiction. Is it the number of deductive steps to reach a contradiction, or the total number of symbols in a proof of contradiction?
Consider for instance two sentences X and ~X where X contains a billion symbols … Is that a contradiction of length 1, or a contradiction of length about 2 billion? I think you mean about 2 billion. In which case, you will always have PD(s) = 0.5 for sentences s of length greater than D. Right?
It may not be clear what you meant by “length” of contradiction. Is it the number of deductive steps to reach a contradiction, or the total number of symbols in a proof of contradiction?
Consider for instance two sentences X and ~X where X contains a billion symbols … Is that a contradiction of length 1, or a contradiction of length about 2 billion? I think you mean about 2 billion. In which case, you will always have PD(s) = 0.5 for sentences s of length greater than D. Right?