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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).
List of contents
Preface,.- 1 Introduction to Hybrid Logic.- 2 Proof-Theory of Propositional Hybrid Logic .- 3 Tableaus and Decision Procedures for Hybrid Logic .- 4 Comparison to Seligman's Natural Deduction System .- 5 Functional Completeness for a Hybrid Logic .- 6 First-Order Hybrid.- 7 Intensional First-Order Hybrid Logic.- 8 Intuitionistic Hybrid Logic.- 9 Labelled Versus Internalized Natural Deduction .- 10 Why does the Proof-Theory of Hybrid Logic Behave soWell? - References .- Index.
Summary
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).
Additional text
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)
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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)
