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arXiv · 2311.02361

A basic system of paraconsistent Nelsonian logic of conditionals

Grigory K. Olkhovikov
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Abstract

We define a Kripke semantics for a conditional logic based on the propositional logic $\mathsf{N4}$, 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 $\mathsf{N4CK}$, shows strong connections both with the basic intuitionistic logic of conditionals $\mathsf{IntCK}$ introduced earlier in arXiv:2306.10402 and with the $\mathsf{N4}$-based modal logic $\mathsf{FSK}^d$ introduced by S. Odintsov and H. Wansing as one of the possible counterparts to the classical modal system $\mathsf{K}$. We map these connections by looking into the embeddings which obtain between the aforementioned systems.

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Grigory K. Olkhovikov. 2023-11-04. A basic system of paraconsistent Nelsonian logic of conditionals. https://arxiv.org/abs/2311.02361

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