### Abstract

Original language | English |
---|---|

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

Journal | Lecture Notes in Computer Science |

Volume | 10119 |

Publication status | Published - 2017 |

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### Cite this

*Lecture Notes in Computer Science*,

*10119*, 168--182.

**Peirce's Sequent Proofs of Distributivity.** / Pietarinen, Ahti-Veikko; Ma, Minghui.

Research output: Contribution to journal › Article

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

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TY - JOUR

T1 - Peirce's Sequent Proofs of Distributivity

AU - Pietarinen, Ahti-Veikko

AU - Ma, Minghui

PY - 2017

Y1 - 2017

N2 - 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.

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.

M3 - Article

VL - 10119

SP - 168

EP - 182

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -