The informativeness/complexity trade-off in the domain of Boolean connectives

I apply the model of semantic universals in terms of informativeness/complexity trade-off (Kemp, Xu, and Regier, 2018) to Boolean connectives. The model explains the cross-linguistic absence of the connective NAND, once we incorporate theoretical insights from Horn (1972) and Katzir and Singh (2013). The lack of NAND follows if languages optimise the trade-off between (a) simplicity of the lexicon measured in terms of primitive symbols and (b) informativeness of the lexicon measured in terms of accurate transfer of information, given scalar implicature. The analysis demonstrates that the model provides a promising insight into the nature of lexicalisation in logical vocabularies.