Hybrid Logic and its Proof-Theory [electronic resource] /
Braüner, Torben.author.
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).
Description based upon print version of record.
Includes bibliographical references and index.
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).
Logic.
Mathematical logic.
Logic.
Mathematical Logic and Formal Languages.
Mathematical Logic and Foundations.