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

(A->B)∨(B->A)

to intuitionistic propositional logic.[1][4]

## See also

* Intermediate logic

## References

1. ↑ 1.0 1.1 von Plato, Jan (2003). "Skolem's Discovery of Gödel-Dummett Logic". Studia Logica 73 (1): 153–157. doi:10.1023/A:1022997524909. http://link.springer.com/10.1023/A:1022997524909.
2. ↑ Baaz, Matthias; Preining, Norbert; Zach, Richard (2007-06-01). "First-order Gödel logics". Annals of Pure and Applied Logic 147 (1): 23–47. doi:10.1016/j.apal.2007.03.001. ISSN 0168-0072. https://www.sciencedirect.com/science/article/pii/S016800720700019X.
3. ↑ Preining, Norbert (2010). "Gödel Logics – A Survey". Logic for Programming, Artificial Intelligence, and Reasoning. Lecture Notes in Computer Science. 6397. pp. 30–51. doi:10.1007/978-3-642-16242-8_4. ISBN 978-3-642-16241-1. https://link.springer.com/chapter/10.1007/978-3-642-16242-8_4. Retrieved 2 March 2022.
4. ↑ Dummett, Michael (1959). "A propositional calculus with denumerable matrix" (in en). The Journal of Symbolic Logic 24 (2): 97–106. doi:10.2307/2964753. ISSN 0022-4812. https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/propositional-calculus-with-denumerable-matrix/732272974D4555B251B046732D2708BC.

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