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1. When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines

Author

Bonchi, Filippo, Di Giorgio, Alessandro, and Trotta, Davide

Subjects
Mathematics - Category Theory, Computer Science - 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.

Published
2024

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