Proof analysis : a contribution to Hilbert's last problem
 Author/Creator
 Negri, Sara, 1967
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2011.
 Physical description
 xi, 265 p. ; 26 cm.
Access
Contributors
 Contributor
 Von Plato, Jan.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 254261) and indexes.
 Contents

 Machine generated contents note: 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.
 Summary
 "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 selfcontained 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 prooftheoretical 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" Provided by publisher.
 "We shall discuss the notion of proof and then present an introductory example of the analysis of the structure of proofs. The contents of the book are outlined in the third and last section of this chapter. 1.1 The idea of a proof A proof in logic and mathematics is, traditionally, a deductive argument from some given assumptions to a conclusion. Proofs are meant to present conclusive evidence in the sense that the truth of the conclusion should follow necessarily from the truth of the assumptions. Proofs must be, in principle, communicable in every detail, so that their correctness can be checked. Detailed proofs are a means of presentation that need not follow in anyway the steps in finding things out. Still, it would be useful if there was a natural way from the latter steps to a proof, and equally useful if proofs also suggested the way the truths behind them were discovered. The presentation of proofs as deductive arguments began in ancient Greek axiomatic geometry. It took Gottlob Frege in 1879 to realize that mere axioms and definitions are not enough, but that also the logical steps that combine axioms into a proof have to be made, and indeed can be made, explicit. To this purpose, Frege formulated logic itself as an axiomatic discipline, completed with just two rules of inference for combining logical axioms. Axiomatic logic of the Fregean sort was studied and developed by Bertrand Russell, and later by David Hilbert and Paul Bernays and their students, in the first three decades of the twentieth century. Gradually logic came to be seen as a formal calculus instead of a system of reasoning: the language of logic was formalized and its rules of inference taken as part of an inductive definition of the class of formally provable formulas in the calculus" Provided by publisher.
 Supplemental links
 Cover image
Subjects
 Subject
 Proof theory.
Bibliographic information
 Publication date
 2011
 Responsibility
 Sara Negri, Jan von Plato.
 ISBN
 9781107008953
 1107008956