A Neutrosophic Categorical Framework for Causal Modeling of Chinese Traditional Cultural Indicators in College Ethnic Instrumental Music Pedagogy

This paper introduces a novel integration of Neutrosophic Logic and Category Theory to model causal relationships between traditional Chinese cultural indicators and educational outcomes in college ethnic instrumental music pedagogy. Recognizing that cultural transmission within music education is inherently uncertain, we construct a categorical model in which objects represent cultural components and morphisms encode causal pathways each embedded with neutrosophic valuations across degrees of truth (T), indeterminacy (I), and falsity (F). This triple-valued causal structure enables the representation of partially known or contextually ambiguous influences, such as ritual symbolism, tonal interpretation, or behavioral norms, within musical instruction. We define and formalize Neutrosophic Causal Categories, introduce triadic morphisms, and provide a complete algebraic framework for modeling non-deterministic educational phenomena. A case study using representative indicators from Confucian and Taoist traditions demonstrates how the model reveals complex interactions between cultural meaning and learning performance. The proposed structure offers an extensible foundation for both theoretical generalization and applied educational modeling under deep uncertainty.