We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas’ conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system $\mathcal {C}$ which is an extension of the Belnap-Dunn four-valued logic with a conditional operator. Some acceptive extensions of $\mathcal {C}$ are shown to be sound and complete. We also show the finite acceptive model property and decidability of these logics.

中文翻译：

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超一致性条件逻辑

我们通过引入具有接受和拒绝选择函数的新条件模型来开发超一致性逻辑，这些模型是 Chelas 条件模型的变体。接受和拒绝条件替换了条件的真值条件。次一致条件逻辑由一个序列系统 $\mathcal {C}$ 公理化，它是带有条件运算符的 Belnap-Dunn 四值逻辑的扩展。$\mathcal {C}$ 的一些可接受的扩展被证明是健全和完整的。我们还展示了这些逻辑的有限接受模型属性和可判定性。