In this paper, we delve into the study of epistemic logics, interpreted through similarity models based on weighted graphs. We explore eight languages that extend the traditional epistemic language by incorporating modalities of common, distributed, and mutual knowledge. The concept of individual knowledge is redefined under these similarity models. It is no longer just a matter of personal knowledge, but is now enriched and understood as knowledge under the individual's epistemic ability. Common knowledge is presented as higher-order knowledge that is universally known to any degree, a definition that aligns with existing literature. We reframe distributed knowledge as a form of knowledge acquired by collectively leveraging the abilities of a group of agents. In contrast, mutual knowledge is defined as the knowledge obtained through the shared abilities of a group. We then focus on the resulting logics, examining their relative expressivity, semantic correspondence to the classical epistemic logic, proof systems and the computational complexity associated with the model checking problem and the satisfiability/validity problem. This paper offers significant insights into the logical analysis and understanding of these enriched forms of knowledge, contributing to the broader discourse on epistemic logic.

翻译：本文深入研究了基于加权图相似性模型解释的认识逻辑。我们探讨了八种扩展传统认识逻辑的语言，通过引入共同知识、分布知识和互知等模态概念。在这些相似性模型下，个体知识的概念被重新定义：它不再仅是个人知识问题，而是被丰富并理解为个体认识能力下的知识。共同知识被呈现为一种高阶知识，它在任何程度上都是普遍已知的，这一定义与现有文献一致。我们将分布知识重新定义为通过集体利用一组智能体的能力所获得的知识形式。相比之下，互知则是通过一组智能体的共享能力所获得的知识。我们随后聚焦于由此产生的逻辑系统，考察它们的相对表达能力、与经典认识逻辑的语义对应关系、证明系统，以及模型检验问题和可满足性/有效性问题的计算复杂性。本文为这些丰富知识形式的逻辑分析与理解提供了重要见解，推动了关于认识逻辑的更广泛讨论。