@inproceedings{0da8e55a50734045a33a8835af4a8feb,
title = "Peirce{\textquoteright}s sequent proofs of distributivity",
abstract = "Peirce{\textquoteright}s 1880 work on the algebra of logic resulted in a successful calculus (PC) for Boolean algebra. Its leading principle (Peirce{\textquoteright}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{\textquoteright}s Rule in PC. The system PC is here presented as a sequent calculus, which was also Peirce{\textquoteright}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.",
keywords = "Alpha graphs, Distributivity, Peirce{\textquoteright}s rule, Sequent calculus",
author = "Minghui Ma and Pietarinen, {Ahti Veikko}",
note = "Funding Information: A. Pietarinen—The work is supported by the Academy of Finland (project 1270335) and the Estonian Research Council (project PUT 1305) (Principle Investigator A.-V. Pietarinen). Funding Information: M. Ma—The work is supported by the National Foundation for Social Sciences and Humanities (grant no. 16CZX049). Publisher Copyright: {\textcopyright} Springer-Verlag GmbH Germany 2017.; 7th Indian Conference on Logic and Its Applications, ICLA 2017 ; Conference date: 05-01-2017 Through 07-01-2017",
year = "2016",
month = dec,
day = "6",
doi = "10.1007/978-3-662-54069-5_13",
language = "English",
isbn = "9783662540688",
series = "Theoretical Computer Science and General Issues",
publisher = "Springer Berlin Heidelberg",
pages = "168--182",
editor = "Sujata Ghosh and Sanjiva Prasad",
booktitle = "Logic and Its Applications",
edition = "1st",
url = "https://link.springer.com/book/10.1007/978-3-662-54069-5",
}