A logical approach to fuzzy truth hedges ?
The starting point of this paper are the works of Hjek and Vychodil on the axiomatization of truth-stressing and-depressing hedges as expansions of Hjeks BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gdel 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.
truth hedges standard completeness mathematical fuzzy logic t-norm based logics