We propose an abstract conceptual framework for analysing complex security systems using a new notion of modes and mode transitions. A mode is an independent component of a system with its own objectives, monitoring data, algorithms, and scope and limits. The behaviour of a mode, including its transitions to other modes, is determined by interpretations of the mode's monitoring data in the light of its objectives and capabilities -- these interpretations we call beliefs. We formalise the conceptual framework mathematically and, by quantifying and visualising beliefs in higher-dimensional geometric spaces, we argue our models may help both design, analyse and explain systems. The mathematical models are based on simplicial complexes.

翻译：我们提出了一种基于“模式”与“模式转换”这一新概念的抽象概念框架，用于分析复杂安全系统。模式是系统中具有自身目标、监控数据、算法以及适用范围与限度的独立组成部分。模式的行为（包括其向其他模式的转换）取决于根据模式的目标与能力对其监控数据进行解释的结果——我们将这种解释称为“信念”。我们从数学角度形式化该概念框架，并通过在高维几何空间中对信念进行量化与可视化，论证了我们的模型可能有助于系统的设计、分析与解释。该数学模型基于单纯复合形。