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Title: Nelsonian Counterparts of Visser's Logics
Author(s): PETRUKHIN, Yaroslav
Journal: Logique et Analyse
Volume: 259    Date: 2022   
Pages: 215-232
DOI: 10.2143/LEA.259.0.3291803

Abstract :
In this paper, we introduce two new logics which are combinations of Nelson’s paraconsistent logic N4 of constructive falsity with Visser’s basic and formal propositional logics BPL and FPL. BPL and FPL can be embedded by Gödel’s translation to modal logic K4 and provability logic GL, respectively. They have the disjunction property and FPL can be used as a tool of studying provability. Its Nelsonian counterpart NFPL which we present in this paper has the same properties and also constructive falsity and paraconsistency. We formalize Nelsonian counterparts of Visser’s logics via natural deduction systems, develop Kripke semantics for them, embed them into Visser’s and modal logics.

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