Peirce's tutorial on existential graphs

Abstract

In his formal papers on existential graphs (EGs), Peirce tended to obscure the simplicity of EGs with distracting digressions. In MS 514, however, he presented his simplest introduction to the EG syntax, semantics, and rules of inference. This article reproduces Peirce's original words and diagrams with further commentary, explanations, and examples. Unlike the syntax-based approach of most current textbooks, Peirce's method addresses the semantic issues of logic in a way that can be transferred to any notation. The concluding section shows that his rules of inference can clarify the foundations of proof theory and relate diverse methods, such as resolution and natural deduction. To relate EGs to other notations for logic, this article uses the Existential Graph Interchange Format (EGIF), which is a subset of the CGIF dialect of Common Logic. EGIF is a linear notation that can be mapped to and from the Alpha, Beta, and Gamma variants of EGs. It can also be translated to or from other formalisms, algebraic or geometrical.

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The official journal of the International Association for Semiotic Studies, founded in 1969 as one of the first scholarly journals in the field, Semiotica features articles reporting results of research in all branches of semiotic studies, in-depth reviews of selected current literature in the field, and occasional guest editorials and reports. The journal also publishes occasional Special Issues devoted to topics of particular interest.

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