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arXiv · 1607.05120

G\"odel Logic: from Natural Deduction to Parallel Computation

Federico Aschieri·Agata Ciabattoni·Francesco A. Genco
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Abstract

Propositional G\"odel logic extends intuitionistic logic with the non-constructive principle of linearity $A\rightarrow B\ \lor\ B\rightarrow A$. We introduce a Curry-Howard correspondence for this logic and show that a particularly simple natural deduction calculus can be used as a typing system. The resulting functional language enriches the simply typed lambda calculus with a synchronous communication mechanism between parallel processes. Our normalization proof employs original termination arguments and sophisticated proof transformations with a meaningful computational reading. Our results provide a computational interpretation of G\"odel logic as a logic of communicating parallel processes, thus proving Avron's 1991 conjecture.

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Federico Aschieri, Agata Ciabattoni, Francesco A. Genco. 2016-07-18. G\"odel Logic: from Natural Deduction to Parallel Computation. https://arxiv.org/abs/1607.05120

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