what I would have considered a series, is Bioshock 1 and 2 would be the series/sequels. while, Bioshock Infinite would be a completely new series of games for Irrational Games.
I looked at quite a few related questions
From my understanding of Bioshock Infinite, is that it is only related to the other games through a central theme and name. That, Bioshock Infinite, isn't an addition to the series or sequel more of a new series entirely.
So, should Bioshock Infinite be included in the bioshock-series