A Graphical Deep Inference System for Intuitionistic Logic

MINGHUI, Ma; PIETARINEN, Ahti-Veikko

Document Details :

Title: A Graphical Deep Inference System for Intuitionistic Logic
Author(s): MINGHUI, Ma , PIETARINEN, Ahti-Veikko
Journal: Logique et Analyse
Volume: 245 Date: 2019
Pages: 73-114
DOI: 10.2143/LEA.245.0.3285706

Abstract :
A graphical approach to intuitionistic propositional logic is presented. The system GrIn is a deep inference system and it is formulated in terms of Peirce’s existential graphs. GrIn is shown to be sound and complete with respect to the class of all Heyting algebras. Moreover, the system GrIn is shown to be equivalent to the Gentzen sequent calculus G3ip via translations between intuitionistic graphs and intuitionistic formulas. We also discuss the intuitionistic interpretation of logical constants proposed by this graphical approach.

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