Corpus ID: 55702048

Graphical Regular Logic

@article{Fong2018GraphicalRL,
title={Graphical Regular Logic},
author={Brendan Fong and David I. Spivak},
journal={ArXiv},
year={2018},
volume={abs/1812.05765}
}
• Published 2018
• Computer Science, Mathematics
• ArXiv
• Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free regular category $\mathsf{FRg}(\mathrm{T})$ on a set $\mathrm{T}$. From this point of view, regular theories are certain monoidal 2-functors from a suitable 2-category of contexts---the 2-category of relations in $\mathsf{FRg}(\mathrm{T})$---to the 2… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-6 OF 6 CITATIONS

Regular and relational categories: Revisiting 'Cartesian bicategories I'

• Mathematics
• 2019

The Axiom of Choice in Cartesian Bicategories

• Computer Science
• CALCO
• 2019

Cartesian bicategories with choice

• Mathematics, Computer Science
• ArXiv
• 2020
VIEW 1 EXCERPT
CITES BACKGROUND

Montague Semantics for Lambek Pregroups

• Computer Science
• ArXiv
• 2019
VIEW 1 EXCERPT
CITES BACKGROUND

The Logic of Picturing: Wittgenstein, Sellars and Peirce’s EG-beta

• Philosophy
• 2018

• Computer Science, Mathematics
• 2019
VIEW 1 EXCERPT

References

Publications referenced by this paper.
SHOWING 1-10 OF 18 REFERENCES

String diagrams for traced and compact categories are oriented 1-cobordisms

• Mathematics
• 2015

Hypergraph Categories

• Mathematics, Computer Science
• ArXiv
• 2018

Sheaves in Geometry and Logic: A First Introduction to Topos Theory

• Mathematics
• 1992

Monoidal Grothendieck Construction.

• Mathematics
• 2018

A categorical approach to open and interconnected dynamical systems

• Computer Science, Mathematics
• 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• 2016

Categories in Control

• Computer Science, Mathematics, Physics
• 2014

A compositional framework for reaction networks

• Mathematics, Physics
• 2017

A Categorical Semantics of Signal Flow Graphs

• Computer Science
• CONCUR
• 2014