Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, this book presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. The author presents a variety of proof systems for classical and non-classical logics and devotes chapters to proofs of cut theorems and decidability theorems.

Proofs and Proof Theory. Classical First-Order Logic. Variants of the First Sequent Calculi. Sequent Calculi for Non-Classical Logics. Consecution Calculi for Non-Classical Logics. Display Calculi and Hypersequents. Cut Rules and Cut Theorems. Some Other Proof Systems. Applications and Applied Calculi. Appendix. Bibliography. Index.