Hybrid Logic and its Proof-Theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Springer
2011
|
| Series: | Applied Logic Series
37 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 231 S. 37 schw.-w. Tab. 235 mm x 155 mm |
| ISBN: | 9789400700017 |
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MARC
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Record in the Search Index
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Contents
Preface
.
v
1
Introduction to Hybrid Logic
. 1
1.1
Informal Motivation
.
I
1.2
Formal Syntax and Semantics
. 5
1,2.1
Translation into First-Order Logic
. 7
1.3
The Origin of Hybrid Logic in Prior's Work
. 10
1.3.1
Did Prior Reach His Philosophical Goal?
. 14
t.4 The Development Since Prior
. 16
2
Proof-Theory of Prepositional Hybrid Logic
. 21
2.1
The Basics of Natural Deduction Systems
. 21
2.2
Natural Deduction for Prepositional Hybrid Logic
. 25
2.2.1
Conditions on the Accessibility Relation
. 28
2.2.2
Some Admissible Rules
. 30
2.2.3
Soundness and Completeness
. 32
2.2.4
Normalization
. 37
2.2.5
The Form of Normal Derivations
. 43
2.2.6
Discussion
. 46
2.3
The Basics of Gentzen Systems
. 48
2.4
Gentzen Systems for Propositional Hybrid Logic
. 50
2.4.
J
Soundness and Completeness
. 51
2.4.2
The Form of Derivations
. 55
2.4.3
Discussion
.-. 53
2.5
Axiom Systems for Propositional Hybrid Logic
. 54
2.5.1
Soundness and Completeness
. 56
2.5.2
Discussion
.·. 57
3
Tableaus
and Decision Procedures for Hybrid Logic
. 59
3.1
The Basics of Tableau Systems
-----.· · 59
3.2
A tableau System Including the universal Modality
. 62
xii Contents
3.2.1
Tableau
Rules for Hybrid Logic
. 62
3.2.2
Some Properties of the Tableau System
. 64
3.2.3
Systematic Tableau Construction
. 66
3.2.4
The Model Existence Theorem and Decidability
. 68
3.2.5
Tableau
Exampies
. 71
3.3
A Tableau System Not Including the Universal Modality
. 76
3.3.1
A Hybrid-Logical Version of Analytic Cuts
. 80
3.4
The Tableau Systems Reformulated as Gentzen Systems
. 83
3.5
Discussion
. 88
4
Comparison to Seligman's Natural Deduction System
. 91
4.1
The Natural Deduction Systems Under Consideration
. 91
4.1.1
Seligmaďs
Original System
. 93
4.2
Translation from Seligman-Style Derivations
. 95
4.3
Translation to Seligman-Style Derivations
. 97
4.4
Reduction Rules
.101
4.5
Discussion
.106
5
Functional Completeness for a Hybrid Logic
.109
5.1
The Natural Deduction System Under Consideration
.109
5.2
Introduction to Functional Completeness
.112
5.3
The General Rule
Schemas .113
5.3.1
Earlier Work on Functional Completeness
.113
5.3.2
Rule
Schemas
for Hybrid Logic
.117
5.3.3
Normalization and Conservativity
.119
5.4
Functional Completeness
.121
5.5
Discussion
.125
6
First-Order Hybrid Logic
.127
6.1
Introduction to First-Order Hybrid Logic
.127
6.1.
í
Some Remarks on Existence and Quantification
.131
6.1.2
Rigidified Constants
.132
6.1.3
Translation into Two-Sorted First-Order Logic
.135
6.2
Natural Deduction for First-Order Hybrid Logic
.138
6.2.1
Conditions on the Accessibility Relation
.139
6.2.2
Some Admissible Rules
.142
6.2.3
Soundness and Completeness
.143
6.2.4
Normalization
.147
6.2.5
The Form of Normal Derivations
.149
6.3
Axiom Systems for First-Order Hybrid Logic
.150
7
Intensions! First-Order Hybrid Logic
.153
7. [
Introduction to
intensione!
First-Order Hybrid Logic
.153
7.1
Л
Generalized Models
.". 157
7.
1
.2
Translation into Three-Sorted First-Order Logic
.160
7.2
Natural Deduction for Intensions! First-Order Hvbrid Loaic
.163
Contents xiii
7.2.1
Soundness and Completeness: Generalized Models
.164
7.2.2
Soundness and Completeness: Standard Models
.166
7.3
Partial Intensions
.168
8
Intuitionistic Hybrid Logic
.171
8.1
Introduction to Intuitionistic Hybrid Logic
.171
8.1.1
Relation to Many-Valued Semantics
.175
8.1.2
Relation to
Birelational
Semantics
.177
8.1.3
Translation into Intuitionistic First-Order Logic
.178
8.2
Natural Deduction for Intuitionistic Hybrid Logic
.180
8.2.1
Conditions on the Accessibility Relation
.180
8.2.2
An Admissible Rule
.183
8.2.3
Soundness and Completeness
.183
8.2.4
Normalization
.186
8.2.5
The Form of Normal Derivations
.191
8.3
Axiom Systems for Intuitionistic Hybrid Logic
.194
8.4
Axiom Systems for a Paraconsistent Hybrid Logic
.195
8.4.1
Soundness and Completeness
.198
8.5
A Curry-Howard Interpretation of Intuitionistic Hybrid Logic
.200
9
Labelled Versus Internalized Natural Deduction
.203
9.1
A Labelled Natural Deduction System for Modal Logic
.203
9.2
The Internalization Translation
.204
9.3
Reductions
.205
9.4
Comparison of Reductions
.207
9.4.1
A Remark on Normalization
.209
10
Why Does the Proof-Theory of Hybrid Logic Behave So Well?
.211
10.1
The Success Criteria
.211
10.1.1
Standard Systems for Modal Logic
.213
10.1.2
Labelled Systems for Modal Logic
.213
10.2
Why Hybrid-Logical Proof-Theory Behaves So Well
.214
10.3
Comparison to Internalization of Bivalent Semantics
.217
10.4
Some Concluding Philosophical Remarks
. 219
References
. 22
1
Index
.229 |
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| spelling | Braüner, Torben Verfasser aut Hybrid Logic and its Proof-Theory Torben Braüner Dordrecht [u.a.] Springer 2011 XIII, 231 S. 37 schw.-w. Tab. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Applied Logic Series 37 Logik (DE-588)4036202-4 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Logik (DE-588)4036202-4 s Beweistheorie (DE-588)4145177-6 s DE-604 Erscheint auch als Online-Ausgabe 978-94-007-0002-4 Applied Logic Series 37 (DE-604)BV011076498 37 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3524306&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021118834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Braüner, Torben Hybrid Logic and its Proof-Theory Applied Logic Series Logik (DE-588)4036202-4 gnd Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4145177-6 (DE-588)4113937-9 |
| title | Hybrid Logic and its Proof-Theory |
| title_auth | Hybrid Logic and its Proof-Theory |
| title_exact_search | Hybrid Logic and its Proof-Theory |
| title_full | Hybrid Logic and its Proof-Theory Torben Braüner |
| title_fullStr | Hybrid Logic and its Proof-Theory Torben Braüner |
| title_full_unstemmed | Hybrid Logic and its Proof-Theory Torben Braüner |
| title_short | Hybrid Logic and its Proof-Theory |
| title_sort | hybrid logic and its proof theory |
| topic | Logik (DE-588)4036202-4 gnd Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Logik Beweistheorie Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3524306&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021118834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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