A deductive system $\text{L}$ that extends intuitionistic logic, including classical logic and the inconsistent (i.e., trivial) consequence relation with respect to which all formulae are theorems. A deductive system $\text{L}$ that properly extends intuitionistic logic and that classical logic properly extends—i.e., properly intermediate between the two—is known as an intermediate logic. A well-known example is the Gödel-Dummett logic $\text{LC}$ (named for logicians Kurt Gödel (1906–1978) and Michael Dummett (1925–2011)) extending intuitionistic logic by the inclusion of the axiom scheme conditional choice $\left(\phi \to \psi \right)\vee \left(\psi \to \phi \right)$.