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, Proof Theory: Sequent Calculi and Related Formalisms 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. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics. The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.

Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the author presents the most up-to-date research studies. She includes an introduction to combinatory logic before progressing to its central theorems and proofs. The text makes intelligent and well-researched connections between combinatory logic and lambda calculi and presents models and applications to illustrate these connections.

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. "Generalized Galois Logics" develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.