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Hybrid Logic and its Proof-Theory

  • Book
  • © 2011

Overview

Authors:
  1. Torben Braüner

    1. Programming, Logic & Intelligent, Systems Research Group (PLIS), Roskilde University, Roskilde, Denmark

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  • First book-length treatment of hybrid logic and its proof-theory
  • Gives detailed introduction to propositional, first-order, and intuitionistic hybrid logic
  • Gives detailed exposition of deductive systems for hybrid logics, including natural deduction, Gentzen, tableau, and axiom systems
  • Includes philosophical and historical background information

Part of the book series: Applied Logic Series (APLS, volume 37)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction to Hybrid Logic

    • Torben Braüner
    Pages 1-20

  3. Proof-Theory of Propositional Hybrid Logic

    • Torben Braüner
    Pages 21-57

  4. Tableaus and Decision Procedures for Hybrid Logic

    • Torben Braüner
    Pages 59-90

  5. Comparison to Seligman’s Natural Deduction System

    • Torben Braüner
    Pages 91-107

  6. Functional Completeness for a Hybrid Logic

    • Torben Braüner
    Pages 109-126

  7. First-Order Hybrid Logic

    • Torben Braüner
    Pages 127-152

  8. Intensional First-Order Hybrid Logic

    • Torben Braüner
    Pages 153-169

  9. Intuitionistic Hybrid Logic

    • Torben Braüner
    Pages 171-201

  10. Labelled Versus Internalized Natural Deduction

    • Torben Braüner
    Pages 203-210

  11. Why Does the Proof-Theory of Hybrid Logic Behave So Well?

    • Torben Braüner
    Pages 211-220

  12. Back Matter

    Pages 221-231
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Keywords

About this book

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Reviews

From the reviews:

"...the present book is a coherent, unified, and very readable entity.

Throughout the discussion is clear, informative, and natural. It can be recommended as a book to read, as well as to consult, after a basic exposure to hybrid logics.

The book ends with a somewhat philosophical discussion... I will not try to summarize the author’s points. I will say I enjoyed the discussion. And the book."


Melvin Fitting
The Graduate School and University Center
City University of New York
New York, USA

“This book grew out of nine research papers of the author, two of which are coauthored by T. Bolander and, respectively, V. de Paiva. The papers were converted into harmonically synchronized chapters of the book, which will certainly appeal to the reader … . The book contains lots of corresponding results, covering all important cases. … Undoubtedly, Braüner’s monograph fills a gap in the hybrid logic literature in a desirable way.” (Bernhard Heinemann, Zentralblatt MATH, Vol. 1217, 2011)

Authors and Affiliations

  • Programming, Logic & Intelligent, Systems Research Group (PLIS), Roskilde University, Roskilde, Denmark

    Torben Braüner

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