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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., Comment: In Proceedings NCL'24, arXiv:2412.20053

On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic view the other logic? In this paper, we focus on one of the directions, namely how classicists can view intuitionistic logic. To this end, we introduce an expansion of positive intuitionistic logic, both semantically and proof-theoretically, and establish soundness and strong completeness. Moreover, we discuss the interesting status of disjunction, and the possibility of combining classical logic and minimal logic. We also compare our system with the system of Caleiro and Ramos., Comment: In Proceedings NCL 2022, arXiv:2204.06359