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＜図書＞
Hybrid logic and its proof-theory
| 責任表示 | Torben Braüner |
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| シリーズ | Applied logic series ; v. 37 |
| データ種別 | 図書 |
| 出版情報 | Dordrecht : Springer , c2011 |
| 本文言語 | 英語 |
| 大きさ | xiii, 231 p. ; 24 cm |
| 概要 | 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 (wher... 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 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 intuitionistic). Book jacket.続きを見る |
| 目次 | 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. |
| 電子版へのリンク | https://hdl.handle.net/2324/7005657 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図3F 数理独自 | BRAU/70/1 | 2011 |
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033212010005182 |
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書誌詳細
| 一般注記 | Includes bibliographical references (p. 221-228) and index |
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| 著者標目 | Braüner, Torben |
| 分 類 | SG:100 |
| 書誌ID | 1001438329 |
| ISBN | 9789400700017 |
| NCID | BB04454973 |
| 巻冊次 | ISBN:9789400700017 |
| NBN | 10,N34 |
| 登録日 | 2011.01.19 |
| 更新日 | 2017.03.21 |