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

19 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
Externally published	Yes

Scopus Subject Areas

Logic
History and Philosophy of Science

User-Defined Keywords

Alpha graph
Deep inference
Peirce
Sequent calculus

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10.1007/s11225-016-9703-y

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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",

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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.

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KW - Sequent calculus

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Proof Analysis of Peirce’s Alpha System of Graphs

Abstract

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