Learning Analytics (LA) has rapidly expanded through practical and technological innovation, yet its foundational identity has remained theoretically under-specified. This paper addresses this gap by proposing the first axiomatic theory that formally defines the essential structure, scope, and limitations of LA. Derived from the psychological definition of learning and the methodological requirements of LA, the framework consists of five axioms specifying discrete observation, experience construction, state transition, and inference. From these axioms, we derive a set of theorems and propositions that clarify the epistemological stance of LA, including the inherent unobservability of learner states, the irreducibility of temporal order, constraints on reachable states, and the impossibility of deterministically predicting future learning. We further define LA structure and LA practice as formal objects, demonstrating the sufficiency and necessity of the axioms and showing that diverse LA approaches -- such as Bayesian Knowledge Tracing and dashboards -- can be uniformly explained within this framework. The theory provides guiding principles for designing analytic methods and interpreting learning data while avoiding naive behaviorism and category errors by establishing an explicit theoretical inference layer between observations and states. This work positions LA as a rigorous science of state transition systems based on observability, establishing the theoretical foundation necessary for the field's maturation as a scholarly discipline.

翻译：学习分析（LA）通过实践与技术革新迅速扩展，但其基础身份在理论上仍缺乏明确界定。本文通过提出首个公理化理论来填补这一空白，该理论正式定义了LA的基本结构、范围与局限性。该框架源于学习的心理学定义及LA的方法论要求，包含五个公理，分别规定了离散观测、经验构建、状态转移与推断。基于这些公理，我们推导出一组定理与命题，阐明了LA的认识论立场，包括学习者状态的内在不可观测性、时间顺序的不可约简性、可达状态的约束条件，以及确定性预测未来学习的不可能性。我们进一步将LA结构与LA实践定义为形式化对象，证明了公理的充分性与必要性，并表明诸如贝叶斯知识追踪与学习仪表盘等多样化的LA方法均可在此框架下得到统一解释。该理论为设计分析方法与解释学习数据提供了指导原则，同时通过在观测与状态之间建立明确的理论推断层，避免了朴素行为主义与范畴错误。本工作将LA定位为一门基于可观测性的状态转移系统严谨科学，为该领域作为学术学科的成熟奠定了必要的理论基础。