willemien: why? and how is decided which ko ko-intersections are local and which are basic? it looks like the ko-intersection that is open for the player with only one ko open is the local-ko-intersection and all others are basic-ko-intersections. but is this correct under all situations?

Herman: On the rightmost ko, you cannot play a cycle of exactly two consecutive moves, because a move by black captures all white stones. Since being able to play a cycle of exactly two consecutive moves is a requirement for the basic-ko-intersection definition, the square marked intersections aren't basic-ko-intersections. If black takes one of the other kos, then in the resulting position the square marked intersection are basic-ko-intersections, because a two move cycle becomes possible.

RobertJasiek: How to decide? By applying either definition! Is it correct under all situations? What is or is not a ko and its types of ko-intersections might or might not change dynamically from move to move; after each move you have to evaluate afresh quite like you should reevaluate the life and death status of each string afresh.

tapir: Should one call cycles longer than two moves ko, at all?