Quantifier words and their multi-functional(?) parts

Formal semantic analyses often take words to be minimal building blocks for the purposes of compositionality. But various recent theories of morphology and syntax have converged on the view that there is no demarcation line corresponding to the word level. The same conclusion has emerged from the compositional semantics of superlatives. In the spirit of extending compositionality below the word level, this paper explores how a small set of particles (Japanese ka and mo, Chinese dou, and Hungarian vala/vagy, mind, and is) form quantifier words and serve as connectives, additive and scalar particles, question markers, and existential verbs. Our main question is whether the meanings of these particles across the varied environments are highly regular, or they are lexicalized with a variety of different meanings that bear a family resemblance. This paper does not reach definitive conclusions, but it raises analytical possibilities using Boolean semantics and Inquisitive Semantics (the semantics of alternatives). It also draws attention to systematic similarities and some differences between the multiple uses of mo and dou that have not been studied in the literature, and reviews accounts in terms of maximality and additivity.