Convergence of sequence of formulas in n-valued propositional logic

Abstract

Abstract: Convergence in truth degree for a sequence of formulas is defined in n-valued [R0] propositional logic. Properties of convergence in measure and convergence in assignment as well as convergence in truth degree for a given sequence of formulas are studied. Necessary and sufficient conditions for the three kinds of convergences are obtained respectively. In the end, it is proved that the three kinds of convergences for a given sequence of formulas are equivalent to each other when the sequence of formulas is finite atomic.

Key words: logic metric space, convergence in measure, convergence in assignment, convergence in truth degree

摘要： 在[n]值[R0]命题逻辑系统中给出了公式列按真度收敛的定义，研究了公式列按度量收敛、按赋值收敛及按真度收敛的性质，给出了三种收敛各自的充分必要条件，在公式列是有限原子的条件下证明了公式列按度量收敛、按赋值收敛及按真度收敛是相互等价的。

关键词: 逻辑度量空间, 度量收敛, 赋值收敛, 真度收敛

MENG Di, LI Jun. Convergence of sequence of formulas in n-valued propositional logic[J]. Computer Engineering and Applications, 2016, 52(22): 55-58.

蒙頔，李骏. n值命题逻辑中公式列的收敛性[J]. 计算机工程与应用, 2016, 52(22): 55-58.

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Convergence of sequence of formulas in n-valued propositional logic

n值命题逻辑中公式列的收敛性

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