We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our approach relies on previous works of the first author \cite{lewjlc2, lewigpl, lewapal} who introduced a modal system containing $S5$-style principles for the reasoning about intutionistic truth (i.e. \textit{proof}) and, inspired by \cite{artpro}, combined that system with concepts of \textit{intuitionistic} belief and knowledge. We consider that combined system and replace the constructive concept of \textit{proof} with a classical notion of \textit{evidence}. This results in a logic that combines modal system $S5$ with classical epistemic principles where $\square\varphi$ reads as `$\varphi$ is evident' in an epistemic sense. Inspired by \cite{lewapal}, and in contrast to the usual possible worlds semantics found in the literature, we propose here a relational, frame-based semantics where belief and knowledge are not modeled via accessibility relations but directly as sets of propositions (sets of sets of worlds).

翻译：我们提出一个逻辑系统，将众所周知的经典认知概念——信念和知识——与证据概念相结合，使得直观原则“证据产生信念和知识”得以满足。我们的方法基于第一作者先前的工作（\cite{lewjlc2, lewigpl, lewapal}），该工作引入了一个包含$S5$式原则的模态系统，用于推理直觉主义真理（即“证明”），并在\cite{artpro}的启发下，将该系统与“直觉主义”信念和知识的概念相结合。我们考虑这一组合系统，并将建构性的“证明”概念替换为经典的“证据”概念。由此产生了一个逻辑，它将模态系统$S5$与经典认知原则相结合，其中$\square\varphi$在认知意义上解读为“$\varphi$是显然的”。受\cite{lewapal}启发，与文献中常见的可能世界语义学不同，我们在此提出一种基于关系框架的语义学，其中信念和知识并非通过可达关系建模，而是直接作为命题集合（世界集合的集合）进行建模。