The basic quasi-Boolean negation (QB-negation) expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics.

中文翻译：

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相关逻辑的基本拟布尔扩展

定义了包括在Anderson和Belnap的关联逻辑R中的关联逻辑的基本拟布尔取反（QB-negation）展开。我们考虑QB否定的两种类型：H否定和D否定。前者具有超直觉性或超直觉性，后一种在某种意义上具有双重直觉性。赋予H否定的逻辑是超完整的。D取反的逻辑是矛盾的。本文中定义的所有逻辑均具有Routley-Meyer三元关系语义。