Proof Analysis
A Contribution to Hilbert's Last Problem

Presents a new way of applying the methods of proof theory to axiomatic theories and systems of philosophical logic.

Sara Negri (Author), Jan von Plato (Author)

9781107417236, Cambridge University Press

Paperback / softback, published 12 June 2014

278 pages
24.4 x 17 x 1.5 cm, 0.45 kg

"...provide a substantial contribution to the development of proof theory in mathematics.... The book covers a lot of useful material in a concise, efficient and very clearly structured manner. The chapters are written with a palpable intention to show how vast the applicability of the methods is. The results are uniform, general and require a high-level preparation in many different fields. This book can be seen as the stimulating continuation of the authors’ introductory book Structural Proof Theory..."
--F. Poggiolesi, Institut d'Histoire et Philosophie des Sciences, Paris, France, History and Philosophy of Logic

This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.

Prologue: Hilbert's Last Problem
1. Introduction
Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction
3. Axiomatic systems
4. Order and lattice theory
5. Theories with existence axioms
Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus
7. Linear order
Part III. Proof Systems for Geometric Theories: 8. Geometric theories
9. Classical and intuitionistic axiomatics
10. Proof analysis in elementary geometry
Part IV. Proof Systems for Nonclassical Logics: 11. Modal logic
12. Quantified modal logic, provability logic, and so on
Bibliography
Index of names
Index of subjects.

Subject Areas: Mathematical logic [PBCD], Philosophy of mathematics [PBB], Philosophy: logic [HPL]