The Calculus of Relations as a Foundation for Mathematics
The Calculus of Relations as a Foundation for Mathematics
复制标题
作为数学基础的关系演算
DOI：
10.1007/s10817-006-9062-x
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Givant
中科院分区：
文献类型：
--
作者：
S. Givant
一个无变量的，基于关系演算的方程逻辑（由德摩根，皮尔斯和Schröder在1864-1895年间发展的二元关系理论）被证明为所有数学的发展提供了一个足够的框架。它的表达和演绎能力相当于一个只有三个变量的一阶逻辑系统的表现和演绎能力。因此，三变量一阶逻辑也为数学提供了一个充分的框架。最后，表明的一个变体可以看作是句子逻辑的一个子系统。因此，有一些句子逻辑的子系统足以完成形式化数学的任务。
A variable-free, equational logicbased on the calculus of relations (a theory of binary relations developed by De Morgan, Peirce, and Schröder during the period 1864–1895) is shown to provide an adequate framework for the development of all of mathematics. The expressive and deductive powers ofare equivalent to those of a system of first-order logic with just three variables. Therefore, three-variable first-order logic also provides an adequate framework for mathematics. Finally, it is shown that a variant ofmay be viewed as a subsystem of sentential logic. Hence, there are subsystems of sentential logic that are adequate to the task of formalizing mathematics.