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.

Provides the first-ever comprehensive presentation of the relational definition scheme Gives a comprehensive presentation of Gentzen's internal completeness paradigm Includes dozens of exercises directing students to the theory behind the logical systems they are learning

Autorentext

Curtis Franks is an associate professor of Philosophy at the University of Notre Dame. He has been on the Philosophy faculty at Notre Dame since 2006. He earned B.A. degrees in Mathematics and Philosophy from Rice University in 2000 and a Ph.D. from the University of California in Irvine's Department of Logic and Philosophy of Science in 2006. Since 2019, he has been, with Anand Pillay, co-editor in chief of the Notre Dame Journal of Formal Logic. He is currently the director of Notre Dame's Joint Program in Logic and Foundations of Mathematics.

Inhalt

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