It is not uncommon for a logic to be invented multiple times, hinting at its robustness. This trend is followed also by the expansion BD+ of Belnap-Dunn logic by Boolean negation. Ending up in the same logic, however, does not mean that the semantic interpretations are always the same as well. In particular, different interpretations can bring us to different logics, once the basic setting is moved from a classical one to an intuitionistic one. For BD+, two such paths seem to have been taken; one (BDi) by N. Kamide along the so-called American plan, and another (HYPE) by G. Moisil and H. Leitgeb along the so-called Australian plan. The aim of this paper is to better understand this divergence. This task is approached mainly by (i) formulating a semantics for first-order BD+ that provides an Australian view of the system; (ii) showing connections of the less explored (first-order) BDi with neighbouring systems, including an intermediate logic and variants of Nelson's logics.

翻译：逻辑系统被多次独立发明的情况并不罕见，这暗示了其稳健性。贝尔纳普-邓恩逻辑通过布尔否定的扩展BD+也遵循了这一趋势。然而，最终得到相同逻辑并不意味着语义解释也总是相同。特别是，当基本设定从经典框架转向直觉主义框架时，不同的解释可能将我们引向不同的逻辑系统。对于BD+而言，似乎存在两条这样的路径：一条（BDi）由中出沿着所谓"美国方案"提出，另一条（HYPE）由莫伊西尔和莱特格布沿着所谓"澳大利亚方案"提出。本文旨在更好地理解这种分歧。主要通过以下方式展开研究：(i) 为一阶BD+构建提供澳大利亚视角的语义框架；(ii) 揭示较少被探索的（一阶）BDi与邻近系统（包括中间逻辑及尼尔森逻辑变体）的关联。