 Another issue which theories of impossible worlds disagree on concerns the amount of logical structure such worlds have. This issue affects impossible worlds specifically: there is no correlative issue concerning possible worlds (beyond our choice of logic). Various classes of impossible worlds display different degrees of anarchic logical behavior: as we shall see, non-normal worlds for non-normal modal logics  (section 5.1),  for instance, are such that only modal sentences behave in a non-standard fashion at them, whereas sentences that include just the Boolean operators of classical logic get the standard treatment. Such worlds appear to be logically more structured than fully anarchic “open” worlds  (section 5.3). For, we shall see, even principles of classical logic involving only the extensional, truth-functional connectives can fail at open worlds: their openness consists in their not being closed under any non-trivial logical consequence principle.