Gödel logic explained

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

(A → B) \lor (B → A) to intuitionistic propositional logic.^[4]

See also

• Intermediate logic

Notes and References

1. von Plato . Jan . 2003 . Skolem's Discovery of Gödel-Dummett Logic. . 73 . 1 . 153–157 . 10.1023/A:1022997524909.
2. Baaz . Matthias . Preining . Norbert . Zach . Richard . 2007-06-01 . First-order Gödel logics . . 147 . 1 . 23–47 . 10.1016/j.apal.2007.03.001 . 0168-0072. math/0601147 .
3. Book: Preining . Norbert . Logic for Programming, Artificial Intelligence, and Reasoning . Gödel Logics – A Survey . Lecture Notes in Computer Science . 2010 . 6397 . 30–51 . 10.1007/978-3-642-16242-8_4 . 978-3-642-16241-1 . https://link.springer.com/chapter/10.1007/978-3-642-16242-8_4 . 2 March 2022.
4. Dummett . Michael . 1959 . A propositional calculus with denumerable matrix . . en . 24 . 2 . 97–106 . 10.2307/2964753 . 0022-4812.