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Proof Analysis - Sara Negri, Jan Von Plato

Proof Analysis

A Contribution to Hilbert's Last Problem
Buch | Hardcover
278 Seiten
2011
Cambridge University Press (Verlag)
978-1-107-00895-3 (ISBN)
CHF 157,10 inkl. MwSt
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A continuation of the authors' book Structural Proof Theory, one of the basic sources for all students and researchers on logic. Presents a way of extending the proof theory of pure logic to cover mathematical axiomatic theories and systems of philosophical 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.

Sara Negri is Docent of Logic at the University of Helsinki. She is the author of Structural Proof Theory (Cambridge University Press, 2001, with Jan von Plato) and she has also written several research papers on mathematical and philosophical logic. Jan von Plato is Professor of Philosophy at the University of Helsinki. He is the author of Creating Modern Probability (Cambridge University Press, 1994), the co-author (with Sara Negri) of Structural Proof Theory (Cambridge University Press, 2001) and has written several papers on logic and epistemology.

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.

Verlagsort Cambridge
Sprache englisch
Maße 180 x 254 mm
Gewicht 720 g
Themenwelt Geisteswissenschaften Philosophie Logik
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 1-107-00895-6 / 1107008956
ISBN-13 978-1-107-00895-3 / 9781107008953
Zustand Neuware
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