Volume 35 Issue 3
Mar.  2009
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Du Guoping, Wang Hongguang, Li Na, et al. Paradox of set theory-universal logic[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(3): 376-379. (in Chinese)
Citation: Du Guoping, Wang Hongguang, Li Na, et al. Paradox of set theory-universal logic[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(3): 376-379. (in Chinese)

Paradox of set theory-universal logic

  • Received Date: 26 Mar 2008
  • Publish Date: 31 Mar 2009
  • A general formal language in which the value of formulas can be recursively defined can be given by a sextuple-model for n(2≤n≤n )-valued logic. It constitutes a universal logic system UL 1, which characterizes this kind of logic. Connectives like abstract negation, abstract implication and abstract equivalence can be defined in the system. They are the generalization of negation, implication and equivalence in two valued logic. Applying these connectives, the general forms of Russellian sets-making predicate and Curryian sets-making predicate were developed. In addition, a new type of set-making predicate which only contains equivalence was developed. Applying these three kinds of sets-making predicates, abstraction principle led to paradoxes in general system of finite valued logic, countable infinite valued logic and uncountable infinite valued logic.

     

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  • [1] Meyer R K, Routley R, Dunn J M. Curry’s paradox[J]. Analysis,1979,39:124-128 [2] Moh Shaw-Kwei. Logic paradox for many-valued systems[J]. The Journal of Symbolic Logic,1954,19:37-40 [3] 朱梧槚.数学与无穷观的逻辑基础[M].大连:大连理工大学出版社, 2008:107-123 Zhu Wujia. Logical foundation of mathematics and infinity[M]. Dalian: Dalian University of Technology Press,2008:107-123(in Chinese) [4] 杜国平.经典逻辑与非经典逻辑基础[M].北京:高等教育出版社, 2006 Du Guoping. The basis of classical logic and non-classical logic[M]. Beijing: Higher Education Press, 2006(in Chinese)
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