Details
Hybrid Logic and its Proof-Theory
Applied Logic Series, Band 37
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96,29 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 17.11.2010 |
| ISBN/EAN: | 9789400700024 |
| Sprache: | englisch |
| Anzahl Seiten: | 231 |
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Beschreibungen
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).
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.
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).
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
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