When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines

2024/04/29 by Bonchi, Filippo, Di Giorgio, Alessandro, Trotta, Davide
#Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2404.18795

Abstract

Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and complete. This paper illustrates a correspondence between fo-bicategories and Lawvere's hyperdoctrines. To streamline our proof, we introduce peircean bicategories, which offer a more succinct characterization of fo-bicategories.

Related

• The calculus of neo-Peircean relations
• Diagrammatic Algebra of First Order Logic
• A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine
• Linear Hyperdoctrines and Comodules
• Bicategorical Models of Classical Propositional Logic