We introduce the concept of |$\textit{access-based}$| intuitionistic knowledge which relies on the intuition that agent |$i$| knows |$\varphi$| if |$i$| has found |$\textit{access to a proof}$| of |$\varphi$|⁠. Basic principles are distribution and factivity of knowledge as well as |$\square\varphi\rightarrow K_i\varphi$| and |$K_i(\varphi\vee\psi) \rightarrow (K_i\varphi\vee K_i\psi)$|⁠, where |$\square\varphi$| reads |$`\varphi$| is proved'. The formalization extends a family of classical modal logics (Lewitzka, 2017, Journal of Logic and Computation, 27, 201--212) designed as combinations of |$\mathit{IPC}$| and |$\mathit{CPC}$| and as systems for the reasoning about proof, i.e. intuitionistic truth. We adopt a formalization of common knowledge from (Lewitzka, 2011, Studia Logica, 97, 233--264) and interpret it here as access-based common knowledge. We compare our proposal with recent approaches to intuitionistic knowledge (Artemov and Protopopescu, 2016, The Review of Symbolic Logic, 9, 266--298; Lewitzka, 2019, Annals of Pure and Applied Logic, 170, 218--250) and bring together these different concepts in a unifying semantic framework based on Heyting algebra expansions.

中文翻译：

---

基于访问的直觉知识

我们介绍| $ \ textit {access-based} $ |的概念。直觉知识，它依赖于代理人| $ i $ |的直觉 知道| $ \ varphi $ | 如果| $ i $ | 已发现| $ \ textit {获得证明} $ | 的| $ \ varphi $ |⁠。基本原理是知识的分布和真实性，以及| $ \ square \ varphi \ rightarrow K_i \ varphi $ | 和| $ K_i（\ varphi \ vee \ psi）\ rightarrow（K_i \ varphi \ vee K_i \ psi）$ |⁠，其中| $ \ square \ varphi $ | 读| $`\ varphi $ | 被证明”。形式化扩展了一系列经典的模态逻辑（Lewitzka，2017，Journal of Logic and Computation，27设计的组合，201--212）| $ \ {mathit IPC} $ | 和| $ \ mathit {CPC} $ | 作为证明论证的系统，即直觉真理。我们从（Lewitzka，2011年，采取共同知识的形式化集刊逻，97，233--264），并在这里把它解释为基于访问的常识。我们将我们的建议与直觉知识的最新方法进行了比较（Artemov和Protopopescu，2016年，《符号逻辑的评论》，第9卷，第266--298页; Lewitzka，2019年，《纯粹逻辑与应用逻辑》，第170页）（218--250），并将这些不同的概念集中在基于Heyting代数展开式的统一语义框架中。