Proof Analysis of Peirce’s Alpha System of Graphs

Minghui Ma; Ahti Veikko Pietarinen

doi:10.1007/s11225-016-9703-y

Proof Analysis of Peirce’s Alpha System of Graphs

Minghui Ma^*, Ahti Veikko Pietarinen

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

22 Citations (Scopus)

Abstract

Charles Peirce’s alpha system S_αis reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of S_αis given in terms of two embedding theorems: the system S_αand Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system S_αand Gentzen sequent calculus G3c^∗can be embedded into each other.

Original language	English
Pages (from-to)	625-647
Number of pages	23
Journal	Studia Logica
Volume	105
Issue number	3
Early online date	19 Dec 2016
DOIs	https://doi.org/10.1007/s11225-016-9703-y
Publication status	Published - Jun 2017

Scopus Subject Areas

Logic
History and Philosophy of Science

User-Defined Keywords

Alpha graph
Deep inference
Peirce
Sequent calculus

Access to Document

10.1007/s11225-016-9703-y

Cite this

@article{a568eca95b464f0e9bcdb9eb442c56ec,

title = "Proof Analysis of Peirce{\textquoteright}s Alpha System of Graphs",

abstract = "Charles Peirce{\textquoteright}s alpha system Sα is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of Sα is given in terms of two embedding theorems: the system Sα and Br{\"u}nnler{\textquoteright}s deep inference system for classical propositional logic can be embedded into each other; and the system Sα and Gentzen sequent calculus G3c∗can be embedded into each other.",

keywords = "Alpha graph, Deep inference, Peirce, Sequent calculus",

author = "Minghui Ma and Pietarinen, {Ahti Veikko}",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science Business Media Dordrecht",

year = "2017",

month = jun,

doi = "10.1007/s11225-016-9703-y",

language = "English",

volume = "105",

pages = "625--647",

journal = "Studia Logica",

issn = "0039-3215",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Proof Analysis of Peirce’s Alpha System of Graphs

AU - Ma, Minghui

AU - Pietarinen, Ahti Veikko

PY - 2017/6

Y1 - 2017/6

N2 - Charles Peirce’s alpha system Sα is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of Sα is given in terms of two embedding theorems: the system Sα and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system Sα and Gentzen sequent calculus G3c∗can be embedded into each other.

AB - Charles Peirce’s alpha system Sα is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of Sα is given in terms of two embedding theorems: the system Sα and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system Sα and Gentzen sequent calculus G3c∗can be embedded into each other.

KW - Alpha graph

KW - Deep inference

KW - Peirce

KW - Sequent calculus

UR - http://www.scopus.com/inward/record.url?scp=85006387005&partnerID=8YFLogxK

U2 - 10.1007/s11225-016-9703-y

DO - 10.1007/s11225-016-9703-y

M3 - Journal article

AN - SCOPUS:85006387005

SN - 0039-3215

VL - 105

SP - 625

EP - 647

JO - Studia Logica

JF - Studia Logica

IS - 3

ER -

Proof Analysis of Peirce’s Alpha System of Graphs

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this