Truth-depressing hedges and BL-logic

We show a complete axiomatization of unary connectives interpreted by monotone and superdiagonal truth functions, so-called truth-depressing hedges. These connectives formalize linguistic hedges like “slightly true” and “more or less”. We follow ideas of [P. Hájek, On very true, Fuzzy Sets and Systems 124 (2001) 329–333] and show that BLvt-logic can be enriched by a unary connective for which we can establish strong completeness with respect to the desired interpretation.