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Studia Logica

, Volume 105, Issue 3, pp 625–647 | Cite as

Proof Analysis of Peirce’s Alpha System of Graphs

  • Minghui MaEmail author
  • Ahti-Veikko Pietarinen
Article

Abstract

Charles Peirce’s alpha system \(\mathfrak {S}_\alpha \) 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 \(\mathfrak {S}_\alpha \) is given in terms of two embedding theorems: the system \(\mathfrak {S}_\alpha \) and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system \(\mathfrak {S}_\alpha \) and Gentzen sequent calculus \(\mathbf {G3c}^*\) can be embedded into each other.

Keywords

Peirce Alpha graph Deep inference Sequent calculus 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Philosophy, Institute of Logic and CognitionSun Yat-Sen UniversityGuangzhouChina
  2. 2.Tallinn University of TechnologyTallinnEstonia

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