2015HS: 41015 Proof Theory

Proof theory is one of the four central pillars of mathematical logic, dealing with formal proofs, studying their properties and developing techniques for their representation and simplification. Proof theory and proof-theoretic techniques have important applications in computer science such as, for example, automated theorem proving, artificial intelligence, logical data bases and expert systems, formal verification. In this course we begin with classical first order logic the central and basic area for all sorts of reasoning, introduce the most important framework for formal proofs, and present the central normalization technique. Then we turn to the constructive variant of classical logic and end with the famous “proofs as computations” approach.