Natural Deduction, Hybrid Systems and Modal Logics

Natural Deduction, Hybrid Systems and Modal Logics

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This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
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Product details

  • Paperback | 492 pages
  • 155 x 235 x 26.42mm | 783g
  • Dordrecht, Netherlands
  • English
  • 2010 ed.
  • 20 Tables, black and white; XIV, 492 p.
  • 9400732430
  • 9789400732438

Back cover copy

This volume provides an extensive treatment of Natural Deduction and related types of proof systems, with a focus on the practical aspects of proof methods. The book has two main aims: Its first aim is to provide a systematic and historical survey of the variety of Natural Deduction systems in Classical and Modal Logics. The second aim is to present some systems of hybrid character, mixing Natural Deduction with other kinds of proof methods (including Sequent systems, Tableaux, Resolution). Such systems tend to be more universal and effective, because of the possibility of mixing strategies of proof search from different areas. All necessary background material is provided, in particular, a detailed presentation of Modal Logics, including First-Order Modal and Hybrid Modal Logics. The deduction systems presented in the book may be of interest to working logicians, researchers on automated deduction and teachers of logic.
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Table of contents

Preliminaries.- Standard Natural Deduction.- Other Deductive Systems.- Extended Natural Deduction.- Survey of Modal Logics.- Standard Approach to Basic Modal Logics.- Beyond Basic Logics and Standard Systems.- Labelled Systems in Modal Logics.- Logics of Linear Frames.- Analytic Labelled ND and Proof Search.- Modal Hybrid Logics.- Proof Methods for MHL.
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About Andrzej Indrzejczak

Andrzej Indrzejczak is professor of logic and Head of the Department of General Methodology at the University of Lodz, Poland. His scientific interests include the proof theory for non-classical logics, the philosophy of logic and the methodology of science. He is the author of three books and numerous papers concerned mainly with the investigation of proof techniques for non-classical logics, published e.g. in Bulletin of the Section of Logic, Logic Journal of the IGPL, Logic and Logical Philosophy, Logica Trianguli, and Studia Logica.
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