基于格图像的康托分维与泛逻辑运算

Raster Image Cantor Fractal Dimension and Universal Logic Operation

康托集作为集合论中一个重要内容,在整个数学研究中有着非常重要的作用,它能使许多问题迎刃而解.康托集构造与格图像分维关系很密切.在经典的逻辑系统中,只考虑集合的测度大小,而忽略了它在参考空间中的几何位置.而在泛逻辑中,实际问题中的位置关系会影响二者的逻辑运算结果.本文介绍了格图像的相关概念,并利用格图像来研究康托集的分形特点,在此基础上做出康托集的泛逻辑运算.

Cantor set as an important content of set theory plays a very important role in the mathematical study.Cantor structure is closely related to image dimension.The classical logic considers the measure of set size instead of its geometric position in the reference space.In contrast,universal logic principle considers position in practical issues which may greatly influence the two logical operation results.In this paper,definitions of raster image will be introduced and then fractal Cantor set will be studied based on raster image and therefore universal logic operation of Cantor set will be carried out.