Author(s): Braüner, Torben
Series: Applied logic series 37
Publisher: Springer
Year: 2011
Language: English
Pages: 231
City: New York, Dordrecht
Tags: Proof theory.;Logic, Symbolic and mathematical.
Content: 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.
