Approximation derived from a scalar exclusive particle associating with covert focus: The case of Hebrew be-sax ha-kol

We propose a unifying analysis of two readings - exclusive and approximative - of the Hebrew particle be-sax ha-kol, arguing that under both the particle is a scalar focus sensitive exclusive, expressing a positive and a negative inference, i.e. the truth of its prejacent and the exclusion of stronger focus alternatives, respectively. The difference between the readings is argued to derive from a minimal difference in the overtness vs. covertness of the focus associate of be-sax ha-kol: Whereas the exclusive reading is standardly derived by associating the particle with overt and prosodically marked material, the approximative reading results from its association with the covert pos modifier of gradable expressions, resulting in an "x is pos A, but not maximally A" inference. We show that this approximative reading is only licensed when the scale associated with the gradable expression is upper-bound, but the standard of comparison is not necessarily maximal, pace Kennedy & McNally (2005), and compare it with the effects of true approximators (like more or less). We also observe that relative to only and to the exclusive reading of be-sax ha-kol, the at-issueness status of the positive and negative components in the approximative reading is reversed, being at-issue vs. not-at-issue, respectively. We discuss this observation in light of claims about the mirror imaged status of components of only vs. p-exh in Bassi et al. (2019), and in light of theories arguing for the gradience of at-issueness status and its sensitivity to information structure (e.g. Abrusán 2011; Tonhauser et al. 2018).