We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment of our logics is classical. In order to achieve this feature, we modify the relational semantics for relevant modal logics so that validity in a model is defined as satisfaction throughout a set of designated states that, as far as propositional connectives are concerned, behave like classical possible worlds. The main technical result of the paper is a modular completeness theorem parametrized by the relevant modal logic formalizing the agent's reasoning.

翻译：我们开发了一个缩写逻辑框架,将相关模式逻辑与古典命题逻辑结合起来。在我们的框架里,代理人是按相关模式逻辑进行推理的模型,而我们逻辑的假设碎片则是古典的。为了实现这一特征,我们修改了相关模式逻辑的关联语义,将模型的有效性定义为在一组指定国家中的满意度,就假设连接而言,在一系列指定国家中,其行为方式与可能的传统世界相似。本文的主要技术结果是模块完整性理论对准的理论,该模型逻辑将相关的模式逻辑正式化了代理人的推理。