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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.
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