Focus particles and negative polarity

In this article I discuss constructions i odin NP and daže odin NP ‘even one NP’ in Russian, which are negative polarity items (NPIs), e.g. Petja *(ne) smog rešit’ i / daže ODNU zadaču ‘Petya didn’t manage to solve even one problem’. Only daže-NPIs are grammatical in non-negative environments of NPI licensing, e.g. Každyj, kto rešil ?daže / ??i ODNU zadaču, polučil začët ‘Everyone who solved even one problem got credit’. The same dependence is observed in several other languages: particles with additive and coordinative functions (like i ‘even, and’) form NPIs with narrower distribution than plain scalar particles (like daže ‘even’). The following question is thus the main topic of the paper: (A) why do i- and daže-NPIs have different distribution? Two auxiliary questions are: (B) what is the semantics of i and daže, and (C) why do they form NPIs when attached to the low endpoint of a scale? I argue that daže triggers only the scalar presupposition and i triggers only the additive presupposition (question B). I show that both scalar and additive presupposition cause ungrammaticality in positive environments (C). Finally, I compare two theories which (aim to) explain why the additive presupposition of i determines a narrower distribution of i-NPIs in comparison to daže-NPIs (A). A simple theory considers ungrammaticality of i-NPIs to be the result of interaction of the additive presupposition with presuppositions of licensing environments. Although it predicts some interpretational differences between i- and daže-NPIs, it fails to explain the confinement of i-NPIs to negative contexts. According to an alternative theory, i-NPIs are subject to standard movement constraints while daže-NPIs take exceptional (i.e. sentential) scope, which explains their different distribution without any additional assumptions. I also show how this theory can explain the weak vs. strong NPIs distinction in other cases.