Data encryption based on godel ' s function 函数的数据加密
2.
The third and the fourth part of this paper is studying the root theory of fuzzy logic and the formalization theory of fuzzy reasoning from the syntactic view 第三部分：讨论了模糊逻辑系统l ~ *和godel中根的理论，以及剩余格值逻辑系统rl中广义mp与多重广义mp的语构理论。
3.
Chapter 4 provides external perspective on the sciences of complexity . we compare them with postmodern sciences , and argue that the unity of science is not possible in the form of the sciences of complexity . many of the most profound achievements of the 20th century science - the theory of relativity , quantum mechanics , godel ' s theorem , chaos theory - prescribe the limits of knowledge 第四章对复杂性科学进行了外部透视，首先把复杂性科学与后现代科学进行比较，二者在反对还原论方面结成了同盟军；其次，经过论证指出复杂性科学不能统一科学，它只能是科学大家庭中的一员；最后，揭示了科学知识、特别是复杂性科学知识的限度。
4.
So r0 operator and godel operator are united in the systems ha the negation - a with respect to parameter a is defined in ha , the many - valued system h1 / 2 = ( [ 0 , 1 ] - 1 / 2 , 1 / 2 ) is discussed in detail . the classification theorem of tautologies in f ( s ) is obtained in h1 / 2 . the classfication of tautologies is defined on hq 本文还在h _系统中引入了带参数的非运算，较细致地研究了多值系统的子代数理论，以为赋值域建立了f ( s )中重言式的分类定理，并将广义重言式分类定理推广到系统h _ ( 0 1 )中。
5.
The paper also analyzes " the undecidable propositions " in the conclusion of godel ' s incompleteness theorem , and finds that they are often mistakenly explained in three ways : propositions whose truth are undistinguishable ; propositions whose truth are uncertain ; and any other propositions than the self - reference and substitution propositions whose truth are unprovable 结论中的“不可判定”命题，现在有三种不同的错误解释：是非不可分辨的命题（三值） 、是非可分辨但不确定的命题（二值） 、除自指代命题之外的是非都不可证的其他命题，它们都不是哥德尔的证法所支持的结论。
