English

When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines

Category Theory 2024-04-30 v1 Logic in Computer Science

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.

Keywords

Cite

@article{arxiv.2404.18795,
  title  = {When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines},
  author = {Filippo Bonchi and Alessandro Di Giorgio and Davide Trotta},
  journal= {arXiv preprint arXiv:2404.18795},
  year   = {2024}
}