自指语句赋值与元胞自动机的动态特征之比较研究
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摘要
Patrick Grim等人运用计算机模拟研究方法,揭示出在?ukasiewicz模糊逻辑系统中自指语句赋值具有周期性和混沌行为等动态特征,而且在系统内混沌行为本身不可判定。元胞自动机同样具有周期性与混沌行为,而Mikhail Prokopenk等人通过构造"自指",证明元胞自动机的动态也同样具有不可判定性。对两者进行比较研究,有助于进一步揭示它们之间的内在关联。
Applying the method of computer modeling,Gary Mar and Patrick Grim showed that in fuzzy logic system self-referential sentences represent periodic and chaotic behavior,and proved that chaos itself is undecidable within the system. Cellular automata also have periodic and chaotic dynamic traits. By constructing"self-reference",it is demonstrated that the dynamic of universal cellular automata is undecidable as well.Comparing the two disciplines will be helpful to reveal the intrinsic relations between them.
Applying the method of computer modeling,Gary Mar and Patrick Grim showed that in fuzzy logic system self-referential sentences represent periodic and chaotic behavior,and proved that chaos itself is undecidable within the system. Cellular automata also have periodic and chaotic dynamic traits. By constructing"self-reference",it is demonstrated that the dynamic of universal cellular automata is undecidable as well.Comparing the two disciplines will be helpful to reveal the intrinsic relations between them.
引文
(1)Gary Mar,Patrick Grim.“Pattern and Chaos:New Images in the Semantics of Paradox”,Nous,Vol.25,1991,pp.659-695.
(2)Mikhail Prokopenko,Michael harre,Joseph Lizier,Fabio Boschetti,Pavlos Pepas,Stuart Kauffman.Self-referential basis of undecidable dynamics:from The Liar Paradox and The Halting Problem to The Edge of Chaos,2019,arX iv:1711.02456v2[cs.LO].
(1)Gary Mar,Patrick Grim.“Pattern and Chaos:New Images in the Semantics of Paradox”,Nous,Vol.25,1991,pp.659-695.
(2)Patrick Grim.“Self-Reference,Chaos,and Fuzzy Logic”,Integration of Fuzzy Logic and Chaos Theory.Edited by Dr.Zhong Li,Wolfgang A Halang,and Guangrong Chen,2006,pp.317-359.
(1)Gary Mar,Patrick Grim.“Pattern and Chaos:New Images in the Semantics of Paradox”,Nous,Vol.25,1991,pp.659-695.
(2)Mikhail Prokopenko,Michael harre,Joseph Lizier,Fabio Boschetti,Pavlos Pepas,Stuart Kauffman.“Self-referential basis of undecidable dynamics:from The Liar Paradox and The Halting Problem to The Edge of Chaos”.2019,arX iv:1711.02456v2[cs.LO].
(1)Petr Hajek,Jeff Paris and John Shepherdson.“The Liar Paradox and Fuzzy Logic”,The Journal of Symbolic Logic,2000(1):339-346.
(2)Andrew Schumann and Florentin Smarandache.Neutrality and Many-Valued Logics.America Researcher Press,2007,pp.65-69.
(2)Mikhail Prokopenko,Michael harre,Joseph Lizier,Fabio Boschetti,Pavlos Pepas,Stuart Kauffman.Self-referential basis of undecidable dynamics:from The Liar Paradox and The Halting Problem to The Edge of Chaos,2019,arX iv:1711.02456v2[cs.LO].
(1)Gary Mar,Patrick Grim.“Pattern and Chaos:New Images in the Semantics of Paradox”,Nous,Vol.25,1991,pp.659-695.
(2)Patrick Grim.“Self-Reference,Chaos,and Fuzzy Logic”,Integration of Fuzzy Logic and Chaos Theory.Edited by Dr.Zhong Li,Wolfgang A Halang,and Guangrong Chen,2006,pp.317-359.
(1)Gary Mar,Patrick Grim.“Pattern and Chaos:New Images in the Semantics of Paradox”,Nous,Vol.25,1991,pp.659-695.
(2)Mikhail Prokopenko,Michael harre,Joseph Lizier,Fabio Boschetti,Pavlos Pepas,Stuart Kauffman.“Self-referential basis of undecidable dynamics:from The Liar Paradox and The Halting Problem to The Edge of Chaos”.2019,arX iv:1711.02456v2[cs.LO].
(1)Petr Hajek,Jeff Paris and John Shepherdson.“The Liar Paradox and Fuzzy Logic”,The Journal of Symbolic Logic,2000(1):339-346.
(2)Andrew Schumann and Florentin Smarandache.Neutrality and Many-Valued Logics.America Researcher Press,2007,pp.65-69.