A basic system of paraconsistent Nelsonian logic of conditionals.

Abstract

We define a Kripke semantics for a conditional logic based on the propositional logic $N4$ , the paraconsistent variant of Nelson's logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting logic, which we call $N4\mathrm{CK}$ , shows strong connections both with the basic intuitionistic logic of conditionals $\mathrm{IntCK}$ introduced earlier in (Olkhovikov, 2023) and with the $N4$ -based modal logic ${\mathrm{FSK}}^d$ introduced in (Odintsov and Wansing, 2004) as one of the possible counterparts to the classical modal system $K$ . We map these connections by looking into the embeddings which obtain between the aforementioned systems.