论文标题
基于访问的直觉知识
Access-based Intuitionistic Knowledge
论文作者
论文摘要
我们介绍了基于访问的直觉知识的概念，该知识依赖于直觉，即代理$ i $知道$φ$，如果$ i $找到了$φ$的证明。基本原理是知识的分布和事实，以及$ \squareφ\ rightArrowk_iφ$和$ k_i（φ\veeψ）\ rightarrow（k_iφ\ veek_iψ）$，其中$ \squareφ$ reads reds reds`$φ$被证明已证明''。形式化扩展了[Lewitzka 2015，2017，2019]在$ ipc $和$ cpc $的组合中设计的古典模态逻辑系列，以及作为证明推理的系统，即直觉真实。我们从[Lewitzka 2011]中采用常识的形式化，并在这里将其解释为基于访问的常识。我们将我们的建议与最新的直觉知识方法进行了比较[Artemov and Protopopescu 2016； Lewitzka 2017，2019]，并在基于Heyting代数扩展的统一语义框架中汇集了这些不同的概念。
We introduce the concept of access-based intuitionistic knowledge which relies on the intuition that agent $i$ knows $φ$ if $i$ has found access to a proof of $φ$. Basic principles are distribution and factivity of knowledge as well as $\squareφ\rightarrow K_iφ$ and $K_i(φ\veeψ) \rightarrow (K_iφ\vee K_iψ)$, where $\squareφ$ reads `$φ$ is proved'. The formalization extends a family of classical modal logics designed in [Lewitzka 2015, 2017, 2019] as combinations of $IPC$ and $CPC$ and as systems for the reasoning about proof, i.e. intuitionistic truth. We adopt a formalization of common knowledge from [Lewitzka 2011] and interpret it here as access-based common knowledge. We compare our proposal with recent approaches to intuitionistic knowledge [Artemov and Protopopescu 2016; Lewitzka 2017, 2019] and bring together these different concepts in a unifying semantic framework based on Heyting algebra expansions.
