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Hybrid logic and its proof-theory

Author: Torben Braüner
Publisher: Dordrecht : Springer, ©2011.
Series: Applied logic series, v. 37.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Braüner, Torben.
Hybrid logic and its proof-theory
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Torben Braüner
ISBN: 9789400700024 9400700024
OCLC Number: 695387415
Description: 1 online resource (xiii, 231 pages).
Contents: 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.
Series Title: Applied logic series, v. 37.
Responsibility: by Torben Braüner.
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Abstract:

Hybrid Logic and its Proof-Theory demonstrates that hybrid-logical proof-theory remedies the lack of uniformity in ordinary modal-logical proof systems. Various versions and proof systems for hybrid  Read more...

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