Proof Analysis
Proof Analysis
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.
- Presents a new approach to structural proof analysis in axiomatic theories and in philosophical logic
- Necessary logical background is covered in the introductory chapters
- Methods of proof analysis are built up gradually with examples that illustrate what can be achieved by their use
Reviews & endorsements
"...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
Product details
June 2014Paperback
9781107417236
278 pages
244 × 170 × 15 mm
0.45kg
Available
Table of Contents
- 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.
