Peirce’s sequent proofs of distributivity

Minghui Ma; Ahti Veikko Pietarinen

doi:10.1007/978-3-662-54069-5_13

Peirce’s sequent proofs of distributivity

Minghui Ma^*, Ahti Veikko Pietarinen

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

11 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Logic and Its Applications
Subtitle of host publication	7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings
Editors	Sujata Ghosh, Sanjiva Prasad
Publisher	Springer Berlin Heidelberg
Pages	168-182
Number of pages	15
Edition	1st
ISBN (Electronic)	9783662540695
ISBN (Print)	9783662540688
DOIs	https://doi.org/10.1007/978-3-662-54069-5_13
Publication status	Published - 6 Dec 2016
Event	7th Indian Conference on Logic and Its Applications, ICLA 2017 - Kanpur, India Duration: 5 Jan 2017 → 7 Jan 2017 https://link.springer.com/book/10.1007/978-3-662-54069-5

Publication series

Name	Theoretical Computer Science and General Issues
Volume	10119
ISSN (Print)	2512-2010
ISSN (Electronic)	2512-2029

Name	ICLA: Indian Conference on Logic and Its Applications

Conference

Conference	7th Indian Conference on Logic and Its Applications, ICLA 2017
Country/Territory	India
City	Kanpur
Period	5/01/17 → 7/01/17
Internet address	https://link.springer.com/book/10.1007/978-3-662-54069-5

Scopus Subject Areas

Theoretical Computer Science
General Computer Science

User-Defined Keywords

Alpha graphs
Distributivity
Peirce’s rule
Sequent calculus

Access to Document

10.1007/978-3-662-54069-5_13

Cite this

Ma, M., & Pietarinen, A. V. (2016). Peirce’s sequent proofs of distributivity. In S. Ghosh, & S. Prasad (Eds.), Logic and Its Applications: 7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings (1st ed., pp. 168-182). (Theoretical Computer Science and General Issues; Vol. 10119), (ICLA: Indian Conference on Logic and Its Applications). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_13

Ma, Minghui ; Pietarinen, Ahti Veikko. / Peirce’s sequent proofs of distributivity. Logic and Its Applications: 7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings. editor / Sujata Ghosh ; Sanjiva Prasad. 1st. ed. Springer Berlin Heidelberg, 2016. pp. 168-182 (Theoretical Computer Science and General Issues). (ICLA: Indian Conference on Logic and Its Applications).

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Ma, M & Pietarinen, AV 2016, Peirce’s sequent proofs of distributivity. in S Ghosh & S Prasad (eds), Logic and Its Applications: 7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings. 1st edn, Theoretical Computer Science and General Issues, vol. 10119, ICLA: Indian Conference on Logic and Its Applications, Springer Berlin Heidelberg, pp. 168-182, 7th Indian Conference on Logic and Its Applications, ICLA 2017, Kanpur, India, 5/01/17. https://doi.org/10.1007/978-3-662-54069-5_13

Peirce’s sequent proofs of distributivity. / Ma, Minghui; Pietarinen, Ahti Veikko.
Logic and Its Applications: 7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings. ed. / Sujata Ghosh; Sanjiva Prasad. 1st. ed. Springer Berlin Heidelberg, 2016. p. 168-182 (Theoretical Computer Science and General Issues; Vol. 10119), (ICLA: Indian Conference on Logic and Its Applications).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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N2 - 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.

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Ma M, Pietarinen AV. Peirce’s sequent proofs of distributivity. In Ghosh S, Prasad S, editors, Logic and Its Applications: 7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings. 1st ed. Springer Berlin Heidelberg. 2016. p. 168-182. (Theoretical Computer Science and General Issues). (ICLA: Indian Conference on Logic and Its Applications). doi: 10.1007/978-3-662-54069-5_13

Peirce’s sequent proofs of distributivity

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