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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.

This paper provides a compositional semantics for the Japanese Q-particle ka that properly accounts for its use in questions, indefinites and disjunctions in a unified fashion. Adopting the two-tier alternative semantics (Rooth 1985;Beck 2006), I will propose that the role of the ka-particle is always to project a set of alternatives introduced by the wh-item in the alternative-semantic dimension to the ordinary-semantic dimension (Kotek 2014). Unlike in previous analyses, I will adopt this semantics for the Q-particle not only for its clause-final use, but also for clause-internal use. Combining this with the cross-categorial existential closure, the analysis accounts for how the interpretation of a ka-ending phrase is conditioned by its syntactic environments. This mechanism enables an account of the previously unexplained parallelism between wh+ka and ka-disjunctions in their variability in interpretations.

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