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.
Kripke completeness of first-order constructive logics with strong negation.Logic Journal of the IGPL, 11(6):615–646, 2003
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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.