The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic B $$_{\text {M}}$$ with a dual intuitionistic negation of the type Sylvan defined for the extension CC $$\omega $$ of da Costa’s paraconsistent logic C $$\omega $$ . We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3 $$_{\text {DH}}$$ , the expansion of G3 $$_{+}$$ with a dual intuitionistic negation of the kind considered by Sylvan (G3 $$_{+}$$ is the positive fragment of Godelian 3-valued logic G3). All logics in the paper are paraconsistent.

中文翻译：

---

G3$$_{\text {DH}}$$ 中包含的基本对偶直觉逻辑及其一些扩展

逻辑 DHb 是扩展 Sylvan 和 Plumwood 的最小 De Morgan 逻辑 B $$_{\text {M}}$$ 的结果，其中包含为扩展 CC $$\omega $$ of da 定义的 Sylvan 类型的双重直觉否定科斯塔的超协调逻辑 C $$\omega $$ 。我们为 Routley-Meyer 三元关系语义提供了一组 DHb 的指定点及其丰富的扩展，包含在 G3 $$_{\text {DH}}$$ 中，G3 $$_{+}$$ 的扩展带有 Sylvan 考虑的那种双重直觉否定（G3 $$_{+}$$ 是哥德尔三值逻辑 G3 的正片断）。论文中的所有逻辑都是超协调的。