Logical Foundations of Proof Complexity

This Book Treats Bounded Arithmetic And Propositional Proof Complexity From The Point Of View Of Computational Complexity. The First Seven Chapters Include The Necessary Logical Background For The Material And Are Suitable For A Graduate Course. Associated With Each Of Many Complexity Classes Are Both A Two-Sorted Predicate Calculus Theory With Induction Restricted To Concepts In The Class And A Propositional Proof System. The Result Is A Uniform Treatment Of Many Systems In The Literature Including BussS Theories For The Polynomial Hierarchy And Many Disparate Systems For Complexity Classes Such As Ac0 Ac0(M) Tc0 Nc1 L Nl Nc And P.