Peirce’s sequent proofs of distributivity

Minghui Ma*, Ahti Veikko Pietarinen

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

11 Citations (Scopus)


Peirce’s 1880 work on the algebra of logic resulted in a successful calculus (PC) for Boolean algebra. Its leading principle (Peirce’s Rule) is that of residuation. We show how the law of distributivity, which Peirce states but does not prove in 1880, can be proved using Peirce’s Rule in PC. The system PC is here presented as a sequent calculus, which was also Peirce’s preferred method. We then give a shorter proof in his 1896 graphical alpha system, and remark on the main findings also of historical importance.

Original languageEnglish
Title of host publicationLogic and Its Applications
Subtitle of host publication7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings
EditorsSujata Ghosh, Sanjiva Prasad
PublisherSpringer Berlin Heidelberg
Number of pages15
ISBN (Electronic)9783662540695
ISBN (Print)9783662540688
Publication statusPublished - 6 Dec 2016
Event7th Indian Conference on Logic and Its Applications, ICLA 2017 - Kanpur, India
Duration: 5 Jan 20177 Jan 2017

Publication series

NameTheoretical Computer Science and General Issues
ISSN (Print)2512-2010
ISSN (Electronic)2512-2029
NameICLA: Indian Conference on Logic and Its Applications


Conference7th Indian Conference on Logic and Its Applications, ICLA 2017
Internet address

Scopus Subject Areas

  • Theoretical Computer Science
  • Computer Science(all)

User-Defined Keywords

  • Alpha graphs
  • Distributivity
  • Peirce’s rule
  • Sequent calculus


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