 Gödel–Dummett logic, also known as Dummett’s LC or simply as Gödel logic, is another early example of a many-valued logic with truth-values in \([0,1]\). It was introduced by Michael Dummett (1959) as the extension of  intuitionistic logic  by the axiom   \[(\varphi \to \psi) \lor (\psi \to \varphi).\]   This formula enforces a linear order in the underlying (Kripke-style as well as algebraic) semantics. It also appears in the context of Kurt Gödel’s observation that it is impossible to characterize intuitionistic logic by finite truth tables (Gödel 1932). In the fuzzy logic setting, Gödel–Dummett logic can alternatively be obtained as an axiomatic extension of MTL by adding the axiom \(\varphi \to \varphi \mathbin{\&amp;} \varphi\), which amounts to requiring the idempotence of \(\&amp;\), and hence the interpretation of both conjunctions coincides. Semantically, Gödel–Dummett logic can also be defined as the consequence relation given by the minimum t-norm. It is distinguished as the only t-norm based logic where the validity of a formula in a given evaluation does not depend on the specific values assigned to the propositional variables, but only on the relative order of these values. In this sense, Gödel–Dummett logic can be seen as a logic of comparative truth. Like for Łukasiewicz logic, the computational complexity of testing validity remains coNP-complete.