 This has led to the development of more stringent algebraic conditions that some polarity items must meet, e.g., anti-additivity (Zwarts 1998). The distribution and licensing of polarity items, subject to widespread variation within and across languages, is an important but extremely complex linguistic phenomenon with implications for the architecture of grammar and the theory of meaning; see Israel 2011, Giannakidou 2011, Chierchia 2013, Horn 2016, and Barker 2018 for extensive discussion and alternative theoretical approaches. Van der Wouden (1996) and Blanchette (2015) provide useful examinations of the connections of negative polarity to negative concord and expletive negation.