冯诺依曼型元胞自动机和自指语句  

Von Neumann-type Cellular Automata and Self-referential Sentences

作　　者：邬舒雯 熊明 Shuwen Wu;Ming Hsiung(School of Philosophy and Social Development, South China Normal University)

机构地区：[1]华南师范大学哲学与社会发展学院

出　　处：《逻辑学研究》2022年第1期46-63,共18页Studies in Logic

基　　金：国家社会科学基金一般项目“语义悖论的可容许模型研究”(19BZX136)资助。

摘　　要：熊明(2020)把初等元胞自动机与自指语句结合起来进行研究,建立起二者在演化过程方面的紧密关联。沿此路径,本文主要考虑一类称为总和型的二维冯诺依曼型元胞自动机,给出其自指语句表达形式。并且通过利用自指语句的性质,寻找元胞自动机相对应的不动点,将其与自指悖论相联系。同时,通过分析其演化过程的(不)稳定性特征,进行了相应的分类。The elementary cellular automata are associated with self-referential sentences(Ming Hsiung,2020),so that a close relationship between them has been established with re-spect to their evolution processes.Along this line,we mainly consider a class of two-dimensional von Neumann-type cellular automata called the totalistic rules,and corre-spond each element of this class to a set of self-referential sentences.And by referring to the properties of self-referential sentences,we determine the fixed points(if any)of the cellular automata that we study,and find some of them have a counterpart to the self-referential paradoxes.At the same time,by analying the(in)stability characteristics of its evolution process,we give a classification of the two-diminsional totalistic von Neumann-type cellular automata.

关 键 词：冯诺依曼型元胞自动机 不动点 修正理论 演化序列 

分 类 号：B81[哲学宗教—逻辑学]