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
Table 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 so well? - References .- Index.