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Native diagrammatic soundness and completeness proofs for Peirce's Existential Graphs (Alpha)

Caterina, Gianluca and Gangle, Rocco and Tohme, Fernando (2022) Native diagrammatic soundness and completeness proofs for Peirce's Existential Graphs (Alpha). [Preprint]

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Abstract

Peirce's diagrammatic system of Existential Graphs (EG) is a logical proof system corresponding to the Propositional Calculus (PL). Most known proofs of soundness and completeness for EG depend upon a translation of Peirce's diagrammatic syntax into that of a suitable Frege-style system. In this paper, drawing upon standard results
but using the native diagrammatic notational framework of the graphs, we present a purely syntactic proof of soundness, and hence consistency, for EG, along with two
separate completeness proofs that are constructive in the sense that we provide an algorithm in each case to construct an EG formal proof starting from the empty Sheet of Assertion, given any expression that is in fact a tautology according to the standard semantics of the system.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Caterina, Gianlucagcaterin@endicott.edu0000-0002-5677-2232
Gangle, Roccorgangle@endicott.edu
Tohme, Fernandoftohme@gmail.com
Keywords: Peirce; existential graphs; diagrammatic logic; completeness; soundness
Subjects: Specific Sciences > Mathematics > Logic
General Issues > History of Philosophy of Science
Depositing User: Dr. Gianluca Caterina
Date Deposited: 24 Sep 2022 17:49
Last Modified: 24 Sep 2022 17:49
Item ID: 21196
Subjects: Specific Sciences > Mathematics > Logic
General Issues > History of Philosophy of Science
Date: 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21196

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