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.
General
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