The origin of relation algebras in the development and axiomatization of the calculus of relations
The origin of relation algebras in the development and axiomatization of the calculus of relations
复制标题
关系代数在关系演算的发展和公理化中的起源
DOI：
10.1007/bf00370681
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发表时间：
1991
期刊：
影响因子：
0.7
通讯作者：
R. Maddux
中科院分区：
文献类型：
--
作者：
R. Maddux
关系演算是由奥古斯都·德·摩根、查尔斯·桑德斯·皮尔斯和恩斯特·施罗德在十九世纪下半叶创建和发展的。 1940 年，阿尔弗雷德·塔斯基 (Alfred Tarski) 提出了大部分关系演算的公理化。在接下来的十年中，塔斯基的公理化导致了关系代数理论的创建，并被罗杰·林登对不可表示关系代数的发现证明是不完整的。本文通过回顾这些历史发展来介绍关系微积分和关系代数理论。
The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and the theory of relation algebras through a review of these historical developments.