This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system.

中文翻译：

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皮尔斯经典命题逻辑演算

本文调查查尔斯·皮尔斯在 1880 年至 1896 年间为经典命题逻辑发展的逻辑演算。Peirce 1880 年在逻辑代数方面的工作为布尔代数带来了成功的演算。这个演算，表示为个人电脑, 在这里被表示为一个连续的微积分而不是一个自然的演绎系统。结果表明，Peirce 的目的是呈现个人电脑作为一个后续的演算。Peirce 在 1880 年提出的分配定律是使用 Peirce 规则证明的，它是一个余数，在个人电脑. Peirce 自 1880 年以来开发的 copula 代数的过渡系统为 1896 年的 alpha 图图形系统铺平了道路。它展示了 alpha 系统的规则如何重新解释布尔代数，回答了 Peirce 的陈述，即逻辑图为逻辑代数提供了一个新的基本假设系统。对两者之间的联系进行了证明理论分析个人电脑和阿尔法系统。