Fuzzy logics with truth hedges revisited
In this paper we build upon previous works of Hajek and Vychodil on the axiomatization of truthstressing and depressing hedges as expansions of BL logic by new unary connectives. They show that their logics are chain-complete, but standard completeness is only proved for the expansions over Godel logic. We propose weaker axiomatizations that have as main advantages the preservation of standard completeness properties of the original logic and the fact that any subdiagonal (resp. superdiagonal) non-decreasing function on [0, 1] preserving 0 and 1 is a sound interpretation of the truth stresser (resp. depresser) connectives.