中文摘要：

提出并证明了在有界闭域上非负且黎曼可积的多元函数的算数平均值极限的黎曼积分形式,还证明了n值R0命题逻辑中当n趋于无穷大时公式的广义真度极限的存在定理;并根据在有界闭域上非负且黎曼可积的多元函数的算数平均值极限的黎曼积分形式和n值R0命题逻辑中当n趋于无穷大时公式的广义真度极限的存在定理,在连续值R0命题逻辑中建立了相对于局部有限理论的公式的广义真度理论,为在R0命题逻辑中建立基于局部有限理论的近似推理,广义积分语义理论等奠定了基础.

英文摘要：

The Riemann integral form of limit of arithmetic mean value of a non-negative and Riemann integrable function with multiple variables in a bounded closed domain is proposed and proved.Secondly,the existence theorem of limit of generalized truth degree of a formula in n-valued R0 propositional logic is obtained.Thirdly,the theory of generalized truth degrees is proposed in continuously valued R0 propositional logic by combining of the Riemann integral form of limit of a-rithmetic mean value of a non-negative and Riemann integrable function with multiple variables in a bounded closed domain and the existence theorem of limit of generalized truth degree of a formula in n-valued R0 propositional logic,which provides the foundation for establishing theories of approximate reasoning and generalized integral semantics based on locally finite theory in R0 propositional logic.