 Others have proposed modal systems where the step leading to 3 in  (37)  is justified while the step leading to 2 is no longer valid, e.g., Aloni 2007, which proposes a uniform account of free choice effects of disjunctions and indefinites under both modals and imperatives. Simons (2005) and Barker (2010) also proposed semantic accounts of free choice inferences, the latter crucially employing an analysis of or in terms of linear logic additive disjunction combined with a representation of strong permission using the deontic reduction strategy (as in Lokhorst 2006).