Context, Judgement, Deduction

11/17/2021
by   Greta Coraglia, et al.
0

We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of judgemental theories. Our analysis sheds light on both the topics, providing a new point of view. In the case of type theory, we provide an abstract definition of type constructor featuring the usual formation, introduction, elimination and computation rules. For natural deduction we offer a deep analysis of structural rules, demystifying some of their properties, and putting them into context. We finish the paper discussing the internal logic of a topos, a predicative topos, an elementary 2-topos et similia, and show how these can be organized in judgemental theories.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/08/2019

A General Framework for the Semantics of Type Theory

We propose an abstract notion of a type theory to unify the semantics of...
12/01/2021

Finitary type theories with and without contexts

We give a definition of finitary type theories that subsumes many exampl...
09/11/2020

A general definition of dependent type theories

We define a general class of dependent type theories, encompassing Marti...
10/25/2020

Graded Modal Dependent Type Theory

Graded type theories are an emerging paradigm for augmenting the reasoni...
04/20/2018

Formalising Mathematics In Simple Type Theory

Despite the considerable interest in new dependent type theories, simple...
07/28/2021

Type theories in category theory

We introduce basic notions in category theory to type theorists, includi...
08/17/2021

Hybrid dynamical type theories for navigation

We present a hybrid dynamical type theory equipped with useful primitive...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.