Proof Analysis : A Contribution to Hilbert's Last Problem

個数：

Proof Analysis : A Contribution to Hilbert's Last Problem

Negri, Sara/ von Plato, Jan

ウェブストア価格 ¥11,118（本体¥10,108）
Cambridge University Press（2014/06発売）
外貨定価 US$ 53.00
ポイント 101pt

オンデマンド(OD/POD)版です。キャンセルは承れません。

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製本 Paperback:紙装版/ペーパーバック版／ページ数 278 p.
言語 ENG
商品コード 9781107417236
DDC分類 511.36

Full Description

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.