Hybrid logic and its proof-theory / by Torben Braüner.
| Author/creator | Braüner, Torben |
| Format | Electronic |
| Publication Info | Dordrecht ; New York : Springer, |
| Description | xiii, 231 p. : ill. ; 24 cm. |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2011 English International |
| Supplemental Content | Full text available from Springer Books |
| Subjects |
| Series | Applied logic series, 1386-2790 ; v. 37. Applied logic series ; v. 37. ^A514223 |
| 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. |
| Bibliography note | Includes bibliographical references (p. 221-228) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2010938944 |
| ISBN | 9789400700017 |
| ISBN | 9400700016 |