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When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines

Authors Filippo Bonchi, Alessandro Di Giorgio , Davide Trotta

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Author Details

Filippo Bonchi
  • University of Pisa, Italy
Alessandro Di Giorgio
  • University College London, UK
Davide Trotta
  • University of Padova, Italy

Funding

  • Bonchi, Filippo: Supported by MUR project PRIN 2022 PNRR No. P2022HXNSC - RAP (Resource Awareness in Programming) and University of Pisa project PRA_2022_99 - FM4HD.
  • Di Giorgio, Alessandro: Supported by EPSRC project EP/V002376/1 - Nominal String Diagrams.

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Filippo Bonchi, Alessandro Di Giorgio, and Davide Trotta. When Lawvere Meets Peirce: An Equational Presentation of Boolean Hyperdoctrines. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.30

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Categorical semantics
Keywords
  • relational algebra
  • hyperdoctrines
  • cartesian bicategories
  • string diagrams

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