Abstract: This paper mainly focuses on the study of the truth degree function theory of formulas in product logic system.The concept of the truth degree function in product logic system is given.Following this，a series of properties of the truth degree function are derived.Moreover，it is important to prove the τ-complete theorem which shows that τ-syntactic and τ-semantics are harmonious．

Key words: truth degree function, τ-theorem, τ-tautology, τ-deduction theorem

摘要： 基于乘积逻辑系统研究公式的真度函数理论。在乘积逻辑系统中给出真度函数的概念，得到真度函数的一系列性质，证明τ-完备性定理，说明τ-语构与τ-语义的和谐性。

关键词: 真度函数, τ-定理, τ-重言式, τ-演绎定理