Epistemic realizability assigns verifier and generator programs to propositions and proves soundness and completeness for minimal, second-order, and higher-order intuitionistic logic.
Then the application ๐ โ ๐ฅ ๐ฝ -reduces to a ๐ฝ-normal form ๐ โ in at most one step, and |๐ โ |ฮโข๐ดโ๐ต โฅ |๐ โ |ฮ,๐ฅ:๐ดโข๐ต
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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.