Sedlár and Vigiani [18] have developed an approach to propositional epistemic logics wherein (i) an agent’s beliefs are closed under relevant implication and (ii) the agent is located in a classical possible world (i.e., the non-modal fragment is classical). Here I construct first-order extensions of these logics using the non-Tarskian interpretation of the quantifiers introduced by Mares and Goldblatt [12], and later extended to quantified modal relevant logics by Ferenz [6]. Modular soundness and completeness are proved for constant domain semantics, using non-general frames with Mares–Goldblatt truth conditions. I further detail the relation between the demand that classical possible worlds have Tarskian truth conditions and incompleteness results in quantified relevant logics.

Sedlár 和 Vigiani [18] 开发了一种命题认知逻辑方法，其中 (i) 主体的信念在相关蕴涵下是封闭的，并且 (ii) 主体位于经典的可能世界中（即，非模态片段是经典的） . 在这里，我使用 Mares 和 Goldblatt [12] 引入的量词的非 Tarskian 解释构建这些逻辑的一阶扩展，后来由 Ferenz [6] 扩展到量化模态相关逻辑。使用具有 Mares–Goldblatt 真值条件的非一般框架，证明了恒定域语义的模块化可靠性和完整性。我进一步详细说明了经典可能世界具有 Tarskian 真值条件的要求与量化相关逻辑的不完整性结果之间的关系。