In this talk I consider the notion of logical duality with regard to some constructive logics. My approach is mainly semantic -- the dualization procedures are based on some important properties of truth values used in constructive logics. In the focus of consideration is an important logic of the constructivist family, constructive logic with strong negation, also known as Nelson's logic of constructible falsity. The logics in question are equipped with suitable proof systems in the form of binary consequence systems, in particular such a system is formulated for Nelson's explosive logic N3. It is shown how this logic can be dualized semantically and syntactically, and how Nelson's logic and its dual can be combined in the general framework of a bi-Nelson logic. In particular, I provide a definition of truth and falsity conditions for the connective of dual Nelson's implication and construct the respective binary consequence proof system in the FMLA-FMLA logical framework. A bi-Nelson logic in a language without implication and dual implication turns out to be the first-degree entailment fragment of the logic R-Mingle, whereas adding implication and dual implication leads to a system similar to Nelson's logic S.