A categorical interpretation of C. S. Peirce's propositional logic Alpha
type: Item
instance of: scholarly article
title: A categorical interpretation of C. S. Peirce's propositional logic Alpha
zbMATH Open document ID: 0953.18002
DOI: 10.1016/S0022-4049(98)00179-0
author: Geraldine Brady
author: Todd H. Trimble
published in: Journal of Pure and Applied Algebra
publication date: 2000-01-01T00:00:00Z
review text: This is an interesting paper, concerning the interaction between propositional logic, geometric topology, and category theory. It is very well summarized in the authors' abstract, which we quote: ``\textit{C. S. Peirce}'s graphical system Alpha for propositional logic is given a geometric representation in term of isotopy classes of planar diagrams, and surgery rules on these diagrams called illative transformations. An algebraic representation theorem is proven, stating that Alpha, as an equational theory, is isomorphic to the theory of Boolean algebras. The geometric and algebraic representations are extended to give multi-sorted analogues of Alpha. An interpretation of Alpha is given in terms of linear logic and the theory of closed categories''.
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 03G05
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 19D23
Mathematics Subject Classification ID: 01A55
zbMATH DE Number: 1472405
zbMATH Keywords: graphical interpretation
zbMATH Keywords: propositional logic
zbMATH Keywords: geometric representation
zbMATH Keywords: illative transformations
zbMATH Keywords: equational theory
zbMATH Keywords: linear logic
zbMATH Keywords: closed categories
reviewed by: Paul Bankston
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00179-0
OpenAlex ID: W2017425972
description: scientific article; zbMATH DE number 1472405