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## Details

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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## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews: "...the present book is a coherent, unified, and very readable entity. Throughout the discussion is clear, informative, and natural. It can be recommended as a book to read, as well as to consult, after a basic exposure to hybrid logics. The book ends with a somewhat philosophical discussion... I will not try to summarize the author's points. I will say I enjoyed the discussion. And the book." Melvin Fitting The Graduate School and University Center City University of New York New York, USA "This book grew out of nine research papers of the author, two of which are coauthored by T. Bolander and, respectively, V. de Paiva. The papers were converted into harmonically synchronized chapters of the book, which will certainly appeal to the reader ... . The book contains lots of corresponding results, covering all important cases. ... Undoubtedly, Brauner's monograph fills a gap in the hybrid logic literature in a desirable way." (Bernhard Heinemann, Zentralblatt MATH, Vol. 1217, 2011) Read more...

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