An Algorithmic Interpretation of a Deep Inference System

Authors:
Kai Brünnler;Richard Mckinley
Affiliations:
Institut für angewandte Mathematik und Informatik, Bern, Switzerland CH --- 3012;Institut für angewandte Mathematik und Informatik, Bern, Switzerland CH --- 3012
Venue:
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2008

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Abstract

We set out to find something that corresponds to deep inference in the same way that the lambda-calculus corresponds to natural deduction. Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained simulation of beta-reduction.