Defining the Scope of Learning Analytics: An Axiomatic Approach for Analytic Practice and Measurable Learning Phenomena

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.