Year: 2021
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Coraglia, Greta, Di Liberti, Ivan
Institutions: Stockholm University, University of Milan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3211912134