Proof Analysis
A Contribution to Hilbert's Last Problem
- Authors:
- Sara Negri, University of Helsinki
- Jan von Plato, University of Helsinki
- Date Published: November 2011
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
- format: Adobe eBook Reader
- isbn: 9781139142823
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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.
Read more- 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
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×Product details
- Date Published: November 2011
- format: Adobe eBook Reader
- isbn: 9781139142823
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
Related Books
related journals
also by this author
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