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.
Dual intuitionistic logic and a variety of negations: The logic of scientific research.Studia Logica: An International Journal for Symbolic Logic, 80(2/3):347–367, 2005
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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.