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 crosslinguistic absence of the connective NAND, once theoretical insights from Horn 1972 and Katzir and Singh 2013 are incorporated. The lack of NAND follows if languages optimize 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 lexicalization in logical vocabularies.