Proof Analysis of Peirce’s Alpha System of Graphs

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.

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Correspondence to Minghui Ma.

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Ma, M., Pietarinen, AV. Proof Analysis of Peirce’s Alpha System of Graphs. Stud Logica 105, 625–647 (2017). https://doi.org/10.1007/s11225-016-9703-y

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Keywords

  • Peirce
  • Alpha graph
  • Deep inference
  • Sequent calculus