A logical approach to fuzzy truth hedges

The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truth-stressing and-depressing hedges as expansions of Hájek’s BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gödel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages: (i) they preserve the standard completeness properties of the original logic and (ii) 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. Hence, these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense.