Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user interaction patterns that lead to insight or assessing the rigor of reported insights. However, theoretical models can be difficult to apply to existing tools and user studies, often due to discrepancies in how insight and its constituent parts are defined. This paper calls attention to the consistent structures that recur across the visualization literature and describes how they connect multiple theoretical representations of insight. We synthesize a unified formalism for insights using these structures, enabling a wider audience of researchers and developers to adopt the corresponding models. Through a series of theoretical case studies, we use our formalism to compare and contrast existing theories, revealing interesting research challenges in reasoning about a user's domain knowledge and leveraging synergistic approaches in data mining and data management research.

翻译：研究者已提出多种理论模型，用于描述用户与可视化系统交互时产生的洞察。这些表征对于理解洞察发现过程至关重要，例如推断导致洞察的用户交互模式，或评估所报告洞察的严谨性。然而，由于洞察及其构成要素的定义存在差异，理论模型往往难以直接应用于现有工具和用户研究。本文关注可视化文献中反复出现的一致性结构，阐述这些结构如何连接多种洞察理论表征。我们利用这些结构整合出一个统一的洞察形式化体系，使更广泛的研究者和开发者能够采用相应模型。通过一系列理论案例研究，我们运用该形式化体系对现有理论进行比较与对比，揭示了在推断用户领域知识、以及利用数据挖掘与数据管理研究中的协同方法时面临的重大研究挑战。