Epistemic realizability assigns verifier and generator programs to propositions and proves soundness and completeness for minimal, second-order, and higher-order intuitionistic logic.
Hence π=β β 0 π€ β and W[π] β π π€ β , and taking π1 := 0and π2 :=πwe have thatπ=1+π=1+π 1 +π 2, as required
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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.