 There are by now a fair number of empirical studies of how various classes of quantifiers identified by logical or computational means are reflected in terms of learning, understanding, cognitive load, etc. Conversely, linguistic and cognitive facts suggest new theoretical questions. For example, as regards computational complexity, Sevenster (2006) showed that the branching of most as in  (40)  in  section 9  is  intractable.[44]  Subsequently, Szymanik observed that if the operations of resumption and iteration (as in  (38)  and  (36),  respectively) are applied to PTIME quantifiers, the result is again in PTIME, in contrast with branching. Similarly, some forms of reciprocal constructions preserve PTIME computability whereas other don’t: “lifting” exactly five with RECIP as in  (39a)  does, but similarly lifting most as in  (39b)  does not.