Hybrid Logic and its Proof-Theory

Introduction to hybrid logic. Informal motivation ; Formal syntax and semantics ; The origin of hybrid logic in prior's work ; The development since prior -- Proof-theory of propositional hybrid logic. The basics of natural deduction systems ; Natural deduction for propositional hybrid logic ; The basics of Gentzen systems ; Gentzen systems for propositional hybrid logic ; Axiom systems for propositional hybrid logic -- Tableaus and decision procedures for hybrid logic. The basics of tableau systems ; A tableau system including the universal modality ; The tableau systems reformulated as Gentzen systems ; Discussion -- Comparison to Seligman's natural deduction system. The natural deduction systems under consideration ; Translation from Seligman-style derivations ; Translation to Seligman-style derivations ; Reduction rules ; Discussion -- Functional completeness for a hybrid logic. The natural deduction system under consideration ; Introduction to functional completeness ; The general rule schemas ; Functional completeness ; Discussion -- First-order hybrid logic. Introduction to first-order hybrid logic ; Natural deduction for first-order hybrid logic ; Axiom systems for first-order hybrid logic -- Intentional first-order hybrid logic. Introduction to intensional first-order hybrid logic ; Natural deduction for intensional first-order hybrid logic ; Partial intensions -- Intuitionistic hybrid logic. Introduction to intuitionistic hybrid logic ; Natural deduction for intuitionistic hybrid logic ; Axiom systems for intuitionistic hybrid logic ; Axiom systems for a paraconsistent hybrid logic ; A Curry-Howard interpretation of intuitionistic hybrid logic -- Labelled versus internalized natural deduction. A labelled natural deduction system for modal logic ; The internalization translation ; Reductions ; Comparison of reductions -- Why does the proof-theory of hybrid logic behave so well?. The success criteria ; Why hybrid-logical proof-theory behaves so well ; Comparison to internalization of bivalent semantics ; Some concluding philosophical remarks.