Does "cancelled" also count as "finished"?

If a series gets axed with a rushed ending it still counts as finished, if it's cancelled without an ending I won't count them as finished. Special circumstances might apply: if an author dies and the series is discontinued it shouldn't count as finished, but I think it'd make sense to count series such as Black Jack as finished because of its episodic nature and irregular publication. I believe none of the listed manga would have this issue, but this applies to possible future answers.