The proof relies on the fact that once an attack has been defended, it is no longer open. Since D11 requires that every defense be made against an open attack, once an attack has been defended and is closed, no defense will be made against it again. Thus, any attack will be answered at most once.This shows that D10-D11-D13 is a sufficient ruleset to generate IL. I kind of thought one of the results would be trivial; and this was it. I still think that it may be the case that D10-D12-D13 also characterizes IL, but I haven't had time to work further on that conjecture.
Friday, June 10, 2011
The role of D11 and D12 in IL
Thinking more on what I wrote about a few days ago, I'm convinced of the redundancy of D12 ("An attack may be answered at most once") in the presence of D11 ("At any round, a player may defend against only the latest open attack made by the other player"). An easy proof: