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.
A sequent calculus for constructive logic with strong negation as a substructural logic.Bulletin of the Section of Logic, 38(1/2):1–7, 2009
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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.