# Peirce's Sequent Proofs of Distributivity

Research output: Contribution to journalArticle

7 Citations (Scopus)

### Abstract

The leading principle (Peirce's Rule) of Peirce's calculus {\bf PC} is that of residuation. Thus the law of distributivity, which Peirce states but does not prove in 1880, can be proved using the rule in {\bf PC}. We also give a shorter proof in his 1896 alpha system and remark on the main historical findings, including the fact that Peirce's preferred method was to present his PC as a sequent calculus.
Original language English 168--182 Lecture Notes in Computer Science 10119 Published - 2017

Distributivity
Residuation
Sequent Calculus
Calculus

### Cite this

In: Lecture Notes in Computer Science, Vol. 10119, 2017, p. 168--182.

Research output: Contribution to journalArticle

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AB - The leading principle (Peirce's Rule) of Peirce's calculus {\bf PC} is that of residuation. Thus the law of distributivity, which Peirce states but does not prove in 1880, can be proved using the rule in {\bf PC}. We also give a shorter proof in his 1896 alpha system and remark on the main historical findings, including the fact that Peirce's preferred method was to present his PC as a sequent calculus.

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EP - 182

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

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