计算机科学 ›› 2018, Vol. 45 ›› Issue (6A): 69-71.
吴美华,王拥军,杨义川,王潇扬
WU Mei-hua,WANG Yong-jun,YANG Yi-chuan,WANG Xiao-yang
摘要: 从计算机科学中的具体悖论实例出发,使用对角线方法来说明一类悖论的生成机制,并指出自指代现象是悖论产生的深层次原因。传统的应对策略往往采用回避的方式,简单禁止自指代以避免悖论。从量子力学和范畴理论两个新视角出发,给出容纳悖论的新模型。结果表明,从新角度审视悖论不仅可以使悖论在某些新领域得到合理解释,而且能提供认识问题本质的新思维。
中图分类号:
[1]千红.罗素悖论与数学危机[J].中国科技纵横,2002(10):138-140. [2]MARCHAL B.Theoretical computer science and the natural sciences[J].Physics of Life Reviews,2005,2(4):251-289. [3]张建军.逻辑悖论研究引论[M].北京:人民出版社,2014:. [4]KRIPKE S A.Outline of a Theory of Truth[J].Journal of Philosophy,1975,72(19):690-716. [5]YANOFSKY N S.Computability and Complexity of Categorical Structures[OL].http://www.researchgate.net/publication/280243417_Computability_and_Complexity_of_Categorical_Structures. [6]YANOFSKY N S.A Universal Approach to Self-Referential Paradoxes,Incompleteness and Fixed Points[J].Bulletin of Symbolic Logic,2003,9(3):362-386. [7]YUKALOV V I,SORNETTE D.Mathematical basis of quantum decision theory[J].Swiss Finance Institute Research Paper,2008(08-25):1-37. [8]AERTS D,GABORA L,SOZZO S,et al.Quantum Structure in Cognition:Fundamentals and Applications[J].ComputerScien-ce,2011,53(5):314-348. [9]YABLO S.Paradox without Self-Reference[J].Analysis,1993,53(4):251-252. [10]PRIEST G.The Structure of the Paradoxes of Self-Reference [J].Mind,1994,103(409):25-34. [11]SMITH N.The principle of uniform solution (of the paradoxes of self-reference)[J].Mind,2000,109(433):117-122. [12]PARENT T.Paradox with just self-reference[J/OL].http://www.unc.edu/~tparent/d.pdf. [13]杨义川,王拥军.《数理逻辑与集合论》中的对角化原则[J].大学数学,2017,33(1):109-113. [14]ABRAMSKY S,TZEVELEKOS N.Introduction to Categories and Categorical Logic[M]∥Introduction to higher order categorical logic.Cambridge University Press,2011:3-94. |
[1] | 陈志远,黄少滨,韩丽丽. 现代模态逻辑在计算机科学中的应用研究 Research on Applications of Modern Modal Logic in Computer Science 计算机科学, 2013, 40(Z6): 70-76. |
[2] | 周丽丽,李凡长. 基于范畴的数据降维方法 Data Dimension Reduction Based on Category Theory 计算机科学, 2011, 38(9): 242-244. |
[3] | 刘超,王文杰. 一个由接口路径求Hamilton回路的算法研究 Research on Hamiltonian Cycle Based on Path with Interface 计算机科学, 2010, 37(9): 252-256. |
[4] | 熊卫 鞠实儿 罗旭东. 论Dempster—Shafer理论的一个悖论 计算机科学, 2005, 32(8): 145-146. |
[5] | 戴葵 李承祖. 量子力学和量子计算机 计算机科学, 2000, 27(5): 1-4. |
|