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In this talk, I argue that the model of semantic universals and variation in terms of complexity/informativeness trade-off (Kemp & Regier, 2012; Regier et al., 2015; Kemp et al., 2018) is applicable to the domain of Boolean connectives. In particular, I propose that the model explains the cross-linguistic absence of the connective NAND, once we incorporate the theoretical insights from Horn (1972) (cf. also Katzir and Singh, 2013). The lack of NAND follows if languages optimise the trade-off between (a) simplicity of the lexicon mea- sured by the number of propositional logic symbols necessary to express the meaning of the connectives and (b) informativeness of the lexicon measured by how much it facilitates accurate transfer of information, given scalar implicature. This model is essentially a reformulation of the explanations proposed by Horn (1972) and Katzir and Singh (2013), but has advantages over them in two respects: it rules out several unattested inventories that are not ruled out by Horn/K&S and it can be generalised to possible languages consisting of connectives among all 16 boolean connectives, not just the four ‘corners’ of the square of opposition, i.e., AND, OR, NOR, and NAND.