The method of Socratic proofs for normal modal propositional logics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Poznań
Wydawn. Nauk. Uniw. Im. A. Mickiewicza
2007
|
| Schriftenreihe: | Seria Filozofia i logika
101 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 96 S. |
| ISBN: | 9788323218111 |
Internformat
MARC
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| 245 | 1 | 0 | |a The method of Socratic proofs for normal modal propositional logics |c Dorota Leszczyńska |
| 264 | 1 | |a Poznań |b Wydawn. Nauk. Uniw. Im. A. Mickiewicza |c 2007 | |
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| 490 | 1 | |a Seria Filozofia i logika |v 101 | |
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Datensatz im Suchindex
| _version_ | 1804137437025271808 |
|---|---|
| adam_text | Table
of
Contents
Introduction
................................................................................................................................. 7
Chapter
1.
The Method of
Socratic
Proofs for Classical Propositional Calculus
.................. 11
1.1.
Notation
................................................................................................................................. 11
1.2.
Erotetic Calculus E*
.............................................................................................................. 13
1.2.1.
Language L*
............................................................................................................... 13
1.2.2.
The Rules of E*
.......................................................................................................... 14
1.2.3.
Semantical Invertibility of Rules
................................................................................ 18
1.3.
A Right-Sided Approach: Calculus E**
................................................................................ 20
1.3.1.
LanguageL** and the Rules of E**
........................................................................... 20
1.3.2.
Semantical Invertibility
-
Semantical Duality
............................................................ 23
1.4.
The Method of
Socratic
Proofs and Inferential Brotetic Logic
.............................................. 25
Chapter
2.
Erotetic Calculi for Normal Modal Propositional Logics
..................................... 27
2.1.
Language M*
......................................................................................................................... 28
2.1.1.
Syntax of M*
.............................................................................................................. 29
2.1.2.
A Bit of Semantics
...................................................................................................... 30
2.1.3.
Questions of M*: An Intuitive Account of
Socratic
Transformations
......................... 34
2.2.
The Rules of Calculi EL.
Socratic
Transformations via the Rules of EL
............................... 37
2.2.1.
Calculus EK
................................................................................................................. 37
2.2.2.
Calculi
EŁ
................................................................................................................... 40
2.3.
Semantical Invertibility of the Rules of EL. Soundness
......................................................... 44
2.4.
Modal Erotetic Calculi and Inferential Erotetic Logic
........................................................... 49
Chapter
3.
Completeness of Modal Erotetic Calculi
................................................................ 54
3.1.
Paths of
Socratic
Transformations
......................................................................................... 54
3.2.
Permanently Unsuccessful Sequents
..................................................................................... 57
3.3.
Complete
Socratic
Transformations
...................................................................................... 60
3.4.
Countermodels
...................................................................................................................... 66
Chapter
4.
Related Work
........................................................................................................... 73
4.1.
Sequent Calculi
..................................................................................................................... 73
4.2.
Tableau Systems
.................................................................................................................... 74
4.3.
Rasiowa-Sikorski Deduction Systems
................................................................................... 78
4.4.
Natural Deduction
................................................................................................................. 81
4.5.
Labelled Deductive Systems
................................................................................................. 82
Final Remarks
............................................................................................................................ 86
Appendix
...................................................................................................................................... 87
References
.................................................................................................................................... 90
List of symbols
............................................................................................................................. 93
Index of names
............................................................................................................................ 94
Subject index
............................................................................................................................... 95
|
| adam_txt |
Table
of
Contents
Introduction
. 7
Chapter
1.
The Method of
Socratic
Proofs for Classical Propositional Calculus
. 11
1.1.
Notation
. 11
1.2.
Erotetic Calculus E*
. 13
1.2.1.
Language L*
. 13
1.2.2.
The Rules of E*
. 14
1.2.3.
Semantical Invertibility of Rules
. 18
1.3.
A Right-Sided Approach: Calculus E**
. 20
1.3.1.
LanguageL** and the Rules of E**
. 20
1.3.2.
Semantical Invertibility
-
Semantical Duality
. 23
1.4.
The Method of
Socratic
Proofs and Inferential Brotetic Logic
. 25
Chapter
2.
Erotetic Calculi for Normal Modal Propositional Logics
. 27
2.1.
Language M*
. 28
2.1.1.
Syntax of M*
. 29
2.1.2.
A Bit of Semantics
. 30
2.1.3.
Questions of M*: An Intuitive Account of
Socratic
Transformations
. 34
2.2.
The Rules of Calculi EL.
Socratic
Transformations via the Rules of EL
. 37
2.2.1.
Calculus EK
. 37
2.2.2.
Calculi
EŁ
. 40
2.3.
Semantical Invertibility of the Rules of EL. Soundness
. 44
2.4.
Modal Erotetic Calculi and Inferential Erotetic Logic
. 49
Chapter
3.
Completeness of Modal Erotetic Calculi
. 54
3.1.
Paths of
Socratic
Transformations
. 54
3.2.
Permanently Unsuccessful Sequents
. 57
3.3.
Complete
Socratic
Transformations
. 60
3.4.
Countermodels
. 66
Chapter
4.
Related Work
. 73
4.1.
Sequent Calculi
. 73
4.2.
Tableau Systems
. 74
4.3.
Rasiowa-Sikorski Deduction Systems
. 78
4.4.
Natural Deduction
. 81
4.5.
Labelled Deductive Systems
. 82
Final Remarks
. 86
Appendix
. 87
References
. 90
List of symbols
. 93
Index of names
. 94
Subject index
. 95 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:58:47Z |
| indexdate | 2024-07-09T21:12:16Z |
| institution | BVB |
| isbn | 9788323218111 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016360128 |
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| publisher | Wydawn. Nauk. Uniw. Im. A. Mickiewicza |
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| series | Seria Filozofia i logika |
| series2 | Seria Filozofia i logika |
| spelling | The method of Socratic proofs for normal modal propositional logics Dorota Leszczyńska Poznań Wydawn. Nauk. Uniw. Im. A. Mickiewicza 2007 96 S. txt rdacontent n rdamedia nc rdacarrier Seria Filozofia i logika 101 Socrates <470-399 a.C.> - wpływ jhpk Logika symboliczna i matematyczna jhpk Zdanie (logika) jhpk Aussagenlogik (DE-588)4136098-9 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Aussagenlogik (DE-588)4136098-9 s Beweis (DE-588)4132532-1 s DE-604 Leszczyńska-Jasion, Dorota 1980- Sonstige (DE-588)113756802X oth Seria Filozofia i logika 101 (DE-604)BV000017168 101 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016360128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The method of Socratic proofs for normal modal propositional logics Seria Filozofia i logika Socrates <470-399 a.C.> - wpływ jhpk Logika symboliczna i matematyczna jhpk Zdanie (logika) jhpk Aussagenlogik (DE-588)4136098-9 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4136098-9 (DE-588)4132532-1 |
| title | The method of Socratic proofs for normal modal propositional logics |
| title_auth | The method of Socratic proofs for normal modal propositional logics |
| title_exact_search | The method of Socratic proofs for normal modal propositional logics |
| title_exact_search_txtP | The method of Socratic proofs for normal modal propositional logics |
| title_full | The method of Socratic proofs for normal modal propositional logics Dorota Leszczyńska |
| title_fullStr | The method of Socratic proofs for normal modal propositional logics Dorota Leszczyńska |
| title_full_unstemmed | The method of Socratic proofs for normal modal propositional logics Dorota Leszczyńska |
| title_short | The method of Socratic proofs for normal modal propositional logics |
| title_sort | the method of socratic proofs for normal modal propositional logics |
| topic | Socrates <470-399 a.C.> - wpływ jhpk Logika symboliczna i matematyczna jhpk Zdanie (logika) jhpk Aussagenlogik (DE-588)4136098-9 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Socrates <470-399 a.C.> - wpływ Logika symboliczna i matematyczna Zdanie (logika) Aussagenlogik Beweis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016360128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000017168 |
| work_keys_str_mv | AT leszczynskajasiondorota themethodofsocraticproofsfornormalmodalpropositionallogics |