Sequent Calculus: Basics and Applications

This lecture introduces Hilbert Systems as an axiom-oriented formalization of Logic, and contrasts them with the more practical Sequent Calculus. Sequent Calculus is explained as a system for proving statements based on assumptions, with a focus on the Cut Elimination theorem and its applications in proof analysis and consistency. The lecture also covers deduction rules, examples, and practical applications of Sequent Calculus in Intuitionistic Logic.