Intuitionistic Variants of Belnap-Dunn Logic BD+: BDi (American Plan) vs HYPE (Australian Plan)
A study of how the paraconsistent classical system BD+ - Belnap-Dunn logic (FDE) expanded by Boolean negation - splits into two inequivalent intuitionistic counterparts depending on how negation is interpreted: BDi (Kamide, American plan) and HYPE (Moisil and Leitgeb, Australian plan). The paper gives a first-order Australian-plan semantics for BD+ and relates first-order BDi to neighbouring systems, including an intermediate logic and variants of Nelson's constructive logics, to explain the divergence.
2501.00495
This NCL'24 proceedings paper examines why a single classical logic can give rise to distinct intuitionistic counterparts. Its focus is BD+, the expansion of Belnap-Dunn logic (first-degree entailmen…