a b s t r a c tWitnessed Gödel logics are based on the interpretation of ∀ (∃) by minimum (maximum) instead of supremum (infimum). Witnessed Gödel logics appear for many practical purposes more suited than usual Gödel logics as the occurrence of proper infima/suprema is practically irrelevant. In this note we characterize witnessed Gödel logics with absoluteness operator w.r.t. witnessed Gödel logics using a uniform translation.

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We consider GÃűdel logics extended by an operator whose semantics is given by I(o(A)) = min{1, r + I(A)}.The language of propositional GÃűdel logics L p consists of a countably infinite set Var of propositional variables and the connectives ⊥, ⊃, ∧, ∨ with their usual arities. We will consider extensions by a unary connective o, by a unary connective or by both. For any r ∈ [0, 1], a GÃűdel r-interpretation I maps formulas to V such that I(⊥) = 0,