Gentzen's Logical Calculi

The Theory Pamphlet presents Gerhard Gentzen's natural deduction and sequent calculi with emphasis on the theory behind the formalism. Its five chapters serve as an advanced logic textbook, introducing universal properties, proof normalization techniques, and decision procedures for classical, intuitionistic, and linear logics. The same material serves also as a philosophical treatise, describing the meaning of, significance of, and relationships among three different ways to conceptualize the idea of logical completeness. Most of the material featured has never before been presented in a systematic and accessible manner.

Gentzen' s dissertation. - Natural deduction. - Sequent calculus. - Logical completeness. - Before and after Gentzen.