Two intuitionistic paradefinite logics N4C and N4C + are introduced as Gentzen-type sequent calculi. These logics are regarded as a combination of Nelson’s paraconsistent four-valued logic N4 and Wansing’s basic constructive connexive logic C. The proposed logics are also regarded as intuitionistic variants of Arieli, Avron, and Zamansky’s ideal paraconistent four-valued logic 4CC. The logic N4C has no quasi-explosion axiom that represents a relationship between conflation and paraconsistent negation, but the logic N4C + has this axiom. The Kripke-completeness and cut-elimination theorems for N4C and N4C + are proved.

中文翻译：

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带和不带拟爆炸的直觉准定逻辑的 Kripke-完备性和消减定理

引入了两种直观的准定逻辑 N4C 和 N4C + 作为 Gentzen 型连续演算。这些逻辑被视为 Nelson 的超协调四值逻辑 N4 和 Wansing 的基本构造连接逻辑 C 的组合。所提出的逻辑也被视为 Arieli、Avron 和 Zamansky 的理想超协调四值逻辑 4CC 的直觉变体。逻辑 N4C 没有表示混杂和超协调否定之间关系的拟爆炸公理，但逻辑 N4C+ 有这个公理。证明了 N4C 和 N4C+ 的 Kripke 完备性和割消定理。