A bilateral natural deduction system with normalisation and base-extension semantics ensures no formula has both a proof and a refutation, matching Nelson's constructive falsity while extending intuitionistic logic.
Falsification, natural deduction and bi-intuitionistic logic.Jour- nal of Logic and Computation, 26(1):425–450, 07 2013
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Bilateralism with incompatible proofs and refutations
A bilateral natural deduction system with normalisation and base-extension semantics ensures no formula has both a proof and a refutation, matching Nelson's constructive falsity while extending intuitionistic logic.