Proof Theory

Introductory course at MGS 2022

Lecturers: Gianluca Curzi and Marianna Girlando

Proof theory studies proofs as mathematical objects, and operates at the interface between computer science, mathematics and philosophy.
Proof theoy has its historical roots in Aristotle's and Leibniz's idea of formalising and automating inferences and reasoning. In the XX century, proof theory developed into formal discipline, and became the main tool of Hilbert's program, whose goal was to prove the consistency of arithmetic through formalisation of proofs. Gödel's incompleteness theorems marked the failure of Hilbert's program, but not of proof theory, that nowadays finds relevant applications in computer science.

In this course we will introduce the main concepts and tools of proof theory. The general aim is to familiarise students with logic and formal systems, to present the main theoretical results of the discipline, and to offer an overview of the relations of proof theory with other fields, such as theory of computation. This course is intended to be introductory, and no prior knowledge on the topic is expected. The course is meant to prepare students to more advanced topics in proof theory.

Outline of the course

This course consists of 5 lectures and 4 exercise sessions.
The lectures will be structured as follows (to be updated during the week).


(To be updated)

Gianluca Curzi, Marianna Girlando @ MGS 2022