### 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 |
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Pages (from-to) | 168--182 |

Journal | Lecture Notes in Computer Science |

Volume | 10119 |

Publication status | Published - 2017 |

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## Cite this

Pietarinen, A-V., & Ma, M. (2017). Peirce's Sequent Proofs of Distributivity.

*Lecture Notes in Computer Science*,*10119*, 168--182.