Peirce's Logical Graphs for Boolean Algebras and Distributive Lattices.
Peirce's logical graphs provide a completely new diagrammatic logical syntax, which in the present paper is contrasted with the standard linear syntax for classical propositional logic. Peirce's transformation rules of alpha graphs are shown to form a deep inference system for classical propositiona...
| Published in: | Transactions of the Charles S. Peirce Society Vol. 54; no. 3; pp. 320 - 341 |
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| Format: | Article |
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Indiana University Press
Summer2018
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=133736971&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 133736971 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00091774 2HR jtl: Transactions of the Charles S. Peirce Society issn: 00091774 maglogo: N pubinfo: dt: Summer2018 vid: 54 iid: 3 pid: 211 pub: Indiana University Press artinfo: ui: 133736971 10.2979/trancharpeirsoc.54.3.02 ppf: 320 ppct: 21 formats: fmt: – @attributes: type: T – @attributes: type: P size: 5.2MB tig: atl: Peirce's Logical Graphs for Boolean Algebras and Distributive Lattices. aug: au: Ma, Minghui affil: Sun Yat-sen University, Guangzhou, China su: Peirce, Charles S. (Charles Sanders), 1839-1914 Syntax (Logic) Boolean algebra Distributive lattices Inferential statistics Sequent calculus Graph theory sug: subj: Peirce, Charles S. (Charles Sanders), 1839-1914 Syntax (Logic) Boolean algebra Distributive lattices Inferential statistics Sequent calculus Graph theory keyword: Boolean algebras C. S. Peirce distributive lattices logical graphs sequent calculus ab: Peirce's logical graphs provide a completely new diagrammatic logical syntax, which in the present paper is contrasted with the standard linear syntax for classical propositional logic. Peirce's transformation rules of alpha graphs are shown to form a deep inference system for classical propositional logic. With the alpha system, Peirce was able to formulate a new diagrammatic approach to Boolean algebras. This is justified by the connection between the alpha system and Peirce's sequent system PC for Boolean algebras. The graphical methodology is extended to the variety of distributive lattices, which shows the flexibility of Peirce's logical graphs. Scrolls of finite arity are introduced to represent the join operation in distributive lattices. A graphical system that is a variant of Peirce's alpha system is introduced for distributive lattices. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Transactions of the Charles S. Peirce Society is the property of Indiana University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Transactions of the Charles S. Peirce Society holder: Indiana University Press dt: @attributes: year: 2018 holdings: @attributes: islocal: N |
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