https://arxiv.org/pdf/2404.18795

When Lawvere meets Peirce: an equational
presentation of boolean hyperdoctrines

by Filippo Bonchi, Alessandro Di Giorgio, Davide Trotta

Pushing algebraization of logic another step forward.

With this approach logical deductions can be made using straightforward equation manipulations.

This kind of bridge will eventually become very useful for knowledge representation!
As knowledge representation is mostly built on description logics, the community so far doesn’t appreciate the potential to enrich its toolset with algebraic methods and other existing mathematical machinery.

#categorytheory #logic #knowledgeRepresentation #cartesianBicategories #relationalAlgebra #Lawvere #Peirce #hyperdoctrines