Overview

From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt­ ing's implication. I have not included anything on entailment, al­ though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun­ damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics.

Full Product Details

Author:   Dov M. Gabbay
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 1981
Volume:   148
Dimensions:   Width: 21.00cm , Height: 1.60cm , Length: 27.90cm
Weight:   0.762kg
ISBN:  

9789048183623

ISBN 10:   9048183626
Pages:   294
Publication Date:   25 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Logical Systems and Semantics.- Introducing HPC.- The Kripke, Beth and Topological Interpretations for HPC.- Heyting’s Propositional Calculus and Extensions.- Three Intermediate Logics.- Formulas in One Variable.- Propositional Connectives.- The Interpolation Theorem.- Second Order Propositional Calculus.- Modified Kripke Interpretation.- Theories in HPC 1.- Theories in HPC 2.- Completeness of HPC with Respect to RE and Post Structures.- Undecidability Results.- Decidability Results.

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