Description:

This is the first booklength treatment of hybrid logic and its prooftheory. 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 prooftheory for ordinary modal logic. Many modallogical 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 hybridlogical prooftheory remedies these deficiencies by giving a spectrum of wellbehaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, firstorder, intensional firstorder, and intuitionistic). Table of Contents Preface,. 1 Introduction to Hybrid Logic. 2 ProofTheory 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 FirstOrder Hybrid. 7 Intensional First Order Hybrid Logic. 8 Intuitionistic Hybrid Logic. 9 Labelled Versus Internalized Natural Deduction . 10 Why does the ProofTheory of Hybrid Logic Behave so well?  References . Index.
