Here, I combine the semantics of Mares and Goldblatt [20] and Seki [29, 30] to develop a semantics for quantified modal relevant logics extending ${\bf B}$ . The combination requires demonstrating that the Mares–Goldblatt approach is apt for quantified extensions of ${\bf B}$ and other relevant logics, but no significant bridging principles are needed. The result is a single semantic approach for quantified modal relevant logics. Within this framework, I discuss the requirements a quantified modal relevant logic must satisfy to be “sufficiently classical” in its modal fragment, where frame conditions are given that work for positive fragments of logics. The roles of the Barcan formula and its converse are also investigated.

在这里，我结合了 Mares 和 Goldblatt [20] 以及 Seki [29, 30] 的语义来开发扩展 ${\bf B}$ 的量化模态相关逻辑的语义。该组合需要证明 Mares–Goldblatt 方法适用于 ${\bf B}$ 和其他相关逻辑的量化扩展，但不需要重要的桥接原则。结果是用于量化模态相关逻辑的单一语义方法。在这个框架内，我讨论了量化模态相关逻辑必须满足的要求，才能在其模态片段中“足够经典”，其中给出了适用于正逻辑片段的框架条件。还研究了 Barcan 公式及其逆公式的作用。