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]}

See also

• Intermediate logic

References

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