Curry-Howard-Lambek Correspondence for Intuitionistic Belief
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This paper introduces a natural deduction calculus for intuitionistic logic of belief 𝖨𝖤𝖫^- which is easily turned into a modal λ-calculus giving a computational semantics for deductions in 𝖨𝖤𝖫^-. By using that interpretation, it is also proved that 𝖨𝖤𝖫^- has good proof-theoretical properties. The correspondence between deductions and typed terms is then extended to a categorial semantics for identity of proofs in 𝖨𝖤𝖫^- showing the general structure of such a modality for belief in an intuitionistic framework.
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