Epistemic realizability assigns verifier and generator programs to propositions and proves soundness and completeness for minimal, second-order, and higher-order intuitionistic logic.
Indeed, since 𝑥 Γ =★ , we know that 𝑥∈dom(Γ) , but if 𝑥 : 𝐴∈dom(Γ) then 𝑥 Γ =✠ 𝐴 ≠★ , contradicting the fact that𝑥 Γ =★
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Verifiers and Generators: Epistemic Semantics for Intuitionistic Logic (Long Version)
Epistemic realizability assigns verifier and generator programs to propositions and proves soundness and completeness for minimal, second-order, and higher-order intuitionistic logic.