On differencies between the explosive and paraconsistent versions of Nelson's logic

Several paraconsistent logics arose from the well-known explosive logics by deleting the axiom ex contradictione quodlibet (ECQ) from their traditional axiomatic. Among such logics are, e.g., the minimal logic and the paraconsistent Nelson's logic, which are paraconsistent versions of the intuitionistic logic and the constructive Nelson's logic with strong negation. The ECQ rejection has many interesting and unexpected consequences that are not so easy to detect. In this talk we give a survey of the algebraic semantics of the paraconsistent Nelson's logic $\mathsf{N4}$ and of the Belnapian modal logic $\mathsf{BS4}$, and discuss differences between paraconsistent and explosive Nelson's logic, which can be seen after passing to topological and modal languages.