Gödel logics with an operator shifting truth values

Abstract

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,