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arXiv · 2006.02417

Curry-Howard-Lambek Correspondence for Intuitionistic Belief

Cosimo Perini Brogi
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Abstract

This paper introduces a natural deduction calculus for intuitionistic logic of belief $\mathsf{IEL}^{-}$ which is easily turned into a modal $\lambda$-calculus giving a computational semantics for deductions in $\mathsf{IEL}^{-}$. By using that interpretation, it is also proved that $\mathsf{IEL}^{-}$ has good proof-theoretic properties. The correspondence between deductions and typed terms is then extended to a categorical semantics for identity of proofs in $\mathsf{IEL}^{-}$ showing the general structure of such a modality for belief in an intuitionistic framework.

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Cosimo Perini Brogi. 2020-06-03. Curry-Howard-Lambek Correspondence for Intuitionistic Belief. https://arxiv.org/abs/2006.02417

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