Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R<sub>0</sub> Propositional Logic System

doi:10.3969/j.issn.0372-2112.2016.08.020

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Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R₀ Propositional Logic System

更新时间：2025-07-08

- Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R₀ Propositional Logic System
- Acta Electronica Sinica Vol. 44, Issue 8, Pages: 1909-1914(2016)
- 作者机构：
  
  陕西师范大学数学与信息科学学院,陕西,西安,710119
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61572016, No.11531009);Fundamental Research Funds for the Central Universities (No.GK201501001)
- DOI：10.3969/j.issn.0372-2112.2016.08.020
  CLC： O141.1
- Published Online：25 August 2016，
  
  Published：2016
- 稿件说明：
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Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R₀ Propositional Logic System[J]. Acta Electronica Sinica, 2016, 44(8): 1909-1914.
DOI：

Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R₀ Propositional Logic System[J]. Acta Electronica Sinica, 2016, 44(8): 1909-1914. DOI： 10.3969/j.issn.0372-2112.2016.08.020.

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

值R

命题逻辑中当

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R

命题逻辑中当

趋于无穷大时公式的广义真度极限的存在定理，在连续值R

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R

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.

Abstract

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

-valued R

propositional logic is obtained.Thirdly

the theory of generalized truth degrees is proposed in continuously valued R

propositional logic by combining of 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 and the existence theorem of li

mit of generalized truth degree of a formula in

-valued R

propositional logic

which provides the foundation for establishing theories of approximate reasoning and generalized integral semantics based on locally finite theory in R

propositional logic.

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Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R0 Propositional Logic System

DOI：10.3969/j.issn.0372-2112.2016.08.020

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Riemann Integral form of Limit of Arithmetic Mean Value of a Function and Its Application in R₀ Propositional Logic System