Gödel logic

In mathematical logic, a Gödel logic, sometimes referred to as Dummett logic or Gödel–Dummett logic,^[1] is a member of a family of finite- or infinite-valued logics in which the sets of truth values V are closed subsets of the unit interval [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics. The concept is named after Kurt Gödel.^[2][3]

In 1959, Michael Dummett showed that infinite-valued propositional Gödel logic can be axiomatised by adding the axiom schema

${\displaystyle (A\rightarrow B)\lor (B\rightarrow A)}$

to intuitionistic propositional logic.^[1][4]