Gödel-Dummett logic

Gödel-Dummett logic is the logic obtained if we extend intuitionistic propositional logic by the axiom

(\varphi \to \psi) \lor (\psi \to \varphi)

Dummett 1959 showed that \varphi is true in Gödel-Dummett logic if and only if it is valid in all Heyting algebras that are finite chains.

Computational interpretation

Federico Aschieri, Agata Ciabattoni, and Francesco A. Genco. 2017. Gödel logic: from natural deduction to parallel computation. In Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS '17). IEEE Press, Article 16, 1–12.

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References

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