Epistemic realizability assigns verifier and generator programs to propositions and proves soundness and completeness for minimal, second-order, and higher-order intuitionistic logic.
Lemma B.4 (Reflexivity).πβ·π Proof.Straightforward by induction onπ.β‘ Lemma B.5 (Substitution).If πβ·π β² and πβ·π β² then π{π₯ := π}β·π β²{π₯:=π β²}
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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.