I show that the logic $\textsf {TJK}^{d+}$ , one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by (i) dropping the requirement that the accessibility relation is reflexive and (ii) only allowing reflexive worlds to serve as counterexamples to logical consequence. In addition, I provide a simplified natural deduction system for $\textsf {TJK}^{d+}$ , in which a restricted form of conditional proof is used to establish conditionals.

中文翻译：

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二进制 KRIPKE 语义为朴素真理提供强大的逻辑

我证明了逻辑 $\textsf {TJK}^{d+}$ 是目前已知的支持朴素真理论的最强逻辑之一，它是通过（i）放弃要求从恒定域直觉逻辑的 Kripke 语义获得的可达性关系是自反的，并且（ii）只允许自反世界作为逻辑结果的反例。此外，我为 $\textsf {TJK}^{d+}$ 提供了一个简化的自然演绎系统，其中使用了一种受限形式的条件证明来建立条件。