数字中医药（英文）2026，Vol.9Issue(3)：317-330,14.DOI:10.1016/j.dcmed.2026.08.001
中医基础理论的形式化、结构化表现及其等价数学表示的构建
Formalization,structural representation,and construction of equivalent mathematical expressions for basic theories of traditional Chinese medicine
摘要
Abstract
Objective To construct a formalized,structured,and equivalent mathematical representa-tion framework for the basic theories of traditional Chinese medicine(TCM),and to illustrate the mathematical expression of the Bianzheng Lunzhi(辨 证 论 治,syndrome differentiation and treatment)process using the Guizhi Tang(桂枝汤)syndrome as an example. Methods Bianzheng(辨 证,syndrome differentiation)attributes and the properties of Chi-nese materia medica(CMM)were selected as the major cognitive elements and were symbol-ized and quantified.The quantified Bianzheng attributes were used to construct a state space,while the effects of CMMs were abstracted as state-correction operators.Within an n-dimen-sional Euclidean space,state attributes,ordering relations,a personalized constitutional baseline,state-transition expressions,and convergence expressions were constructed,and a schematic calculation based on Guizhi Tang syndrome was performed. Results A mathematical representation framework comprising an n-dimensional state space S,a personalized constitutional baseline vector B,a state-correction operator O,a harmoniza-tion coefficient α,and compatibility coefficients λrs was established.A first-order affine state-transition equation and a generalized state-transition equation incorporating nonlinear com-patibility terms were formulated.Under the schematic parameter settings,the initial state of the Guizhi Tang syndrome changed from S1=(2,2,-2,-2)T to S2=(0.8,0.4,-0.4,-0.8)T,while the health index V decreased from 4.00 to 1.26,indicating that the state approached the predefined healthy equilibrium. Conclusion The framework developed in this study can provide a unified,describable,and computable mathematical representation of syndrome states,formula-related therapeutic ac-tions,and state changes in the Bianzheng Lunzhi process.It may provide a foundation for the formal study of the basic theories of TCM and for subsequent calibration using clinical data.关键词
中医数字化/辨证论治/数学形式化/状态空间表示/状态校正算符/状态转移Key words
Digitalization of traditional Chinese medicine/Bianzheng Lunzhi/Mathematical formalization/State-space representation/State-correction operator/State transition引用本文复制引用
董云峰,万雪松,邓科,彭成,罗懋康..中医基础理论的形式化、结构化表现及其等价数学表示的构建[J].数字中医药（英文）,2026,9(3):317-330,14.基金项目
State Key Laboratory of Southwestern Chinese Medicine Resources(SKLTCM202302 and SKLTCM202201). （SKLTCM202302 and SKLTCM202201）
