Proofs and proof theory
Proofs of all kinds
Early history of proof theory in a nutshell
Proofs as calculations
Classical first-order logic
The sequent calculus LK
An axiom system for FOL
Equivalence of LK and K
Interpretations, soundness and completeness
Variants of the first sequent calculi
Intuitionistic logic and other modifications
Sequent calculi with multisets and sets
Sequent calculi with no structural rules
One-sided sequent calculi
Uniform sequent calculi
Disjunction property
Translations between classical and intuitionistic logics
Sequent calculi for non-classical logics
Associative Lambek calculus
Extensions of the associative Lambek calculus
Relevant implication and pure entailment
Non-distributive logic of relevant implication
Linear logic
Positive logic of relevant implication
Sequent calculi for modal logics
Merge calculi
Consecution calculi for non-classical logics
Non-associative Lambek calculus
Structurally free logics
More implicational relevance logics
Positive entailment logics
Calculi with multiple right-hand side
Display calculi and hypersequents
Display logics with star
Display logic for linear logic
Display logic for symmetric gaggles
Hypersequent calculi
Cut rules and cut theorems
Uniform cut theorem
Mix, multiple and single cuts
Constants and the cut
Display cut
Cut theorem via normal proofs
Cut theorem via interpretations
Analytic cut
Consequences of the cut theorem and uses of the cut rules
Some other proof systems
Natural deduction systems
Tableau systems
Resolution systems
Applications and applied calculi
Decidability
Sequent calculi for mathematical theories
Typed and labeled calculi
Appendix: Some supplementary concepts
Bibliography
Index
Biography
Katalin Bimbo
"Katalin Bimbo is one of the leading relevance logicians in the world today and indeed one of the leading non-classical logicians in general. Her book on proof theory takes readers through standard (classical) proof theory and beyond, including proof theory for some of the most important non-classical logics. The discussion is brilliantly executed. All graduate students interested in logic should study this book and all faculty too. I plan to use the book often."
—Jc Beall, Professor of Philosophy, University of Connecticut, and Professorial Fellow, Northern Institute of Philosophy, University of Aberdeen
