Lectures on mathematical logic: 2 Calculi for derivations and deductions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Gordon & Breach
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 322 S. graph. Darst. |
| ISBN: | 9056992678 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
Introduction 1
1. Sequent Calculi for Positive Logic 5
1. Positive Rules for Deductive Situations 5
2. The Calculus KSP 8
3. The Calculi KtP and KUP 11
4. Inversion Operators 19
5. Tableaux 21
2. Cuts 27
1. Cut Elimination with Exchange Operators 29
2. Arithmetization 44
3. Continuous Cut Elimination 46
1. Explicit Retracing as a Motivation 46
2. The Reduction Operator Ro 51
3. The Reduction Operator Rj and the Elimination Operator . . 63
4. Sequent Calculi for Minimal and Intuitionistic Logic 67
1. Negation in Deductive Situations 67
2. The Calculi KM0 of Minimal Logic and KJ0 of Intuitionistic
Logic 69
3. The Intermediary Calculi KM], KJ] 70
4. The Calculi LM and LJ 75
5. K Calculi for the Connective i 83
6. Tableaux 86
5. Sequent Calculi for Classical Logic 88
1. The Multiple Calculus MK 91
2. Cut Elimination with Inversion Rules for MK 97
3. MK as a Calculus for Classical Logic 101
4. The Calculi MP, MM and MJ 107
5. The Peirce Rule 109
6. Tableaux 119
6. Classes of Algebras Associated to a Calculus 126
1. d Algebras and d Frames 126
2. e Algebras, e Frames and RPC Semilattices 134
3. g Algebras, g Frames and RPC Lattices 141
4. m Algebras, m Frames and m Lattices 145
5. i Algebras, i Frames and Heyting Algebras 151
6. c Algebras, c Frames and Boolean Algebras 157
7. Translations from Classical into Intuitionistic Logic 161
vi Contents
7. Calculi of Formulas 168
1. Modus Ponens Calculi for Positive Logic 174
2. Modus Ponens Calculi for Minimal and for
Intuitionistic Logic 181
3. Modus Ponens Calculi for Classical Logic 185
Historical Notes to Chapters 1 7 196
8. Sequent Calculi for Quantifier Logic 202
1. Quantifier Rules for Deductive Situations 202
2. Sequent Calculi with Q rules 204
3. The Replacement Theorem and Cut Elimination for Calculi
with rep 212
4. The Substitution Theorem and Cut Elimination for Calculi
with sub 219
5. The Sets SUB 221
6. The Substitution Theorem Resumed 226
7. Cut Elimination Resumed 231
8. Inversion Rules 233
9. Semantical Consequence Operations and
Modus Ponens Calculi 236
1. The Calculi cxqt and cxqs 236
2. The Variants cxqt0 of cxqt 240
3. The Variants cxqtj and cxqt2 of cxqt 243
4. The Calculi cxqs, 245
5. The Deduction Theorem and Other Metarules for
the Calculi ccqt, 248
6. Tautologies of Positive Quantifier Logic 250
7. Tautologies of Minimal Quantifier Logic 252
8. Tautologies of Classical Quantifier Logic 253
10. Selected Topics in Sequential Quantifier Logic 256
1. Translating Between Sequential and Modus Ponens Calculi . 256
2. Relations between Classical and Intuitionistic Derivability . 259
3. Equality Logic 263
4. Language Extensions with Predicate Symbols 270
5. Language Extensions with Function Symbols 1 274
6. Language Extensions with Function Symbols 2 285
7. The Midsequent Theorem 288
8. Herbrand s Theorem for Prenex Formulas 298
9. Tableaux 305
Index of concepts and names 317
Index of symbolic notations 321
|
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| indexdate | 2024-07-09T18:36:32Z |
| institution | BVB |
| isbn | 9056992678 |
| language | English |
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| publishDate | 2000 |
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| publisher | Gordon & Breach |
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| spelling | Felscher, Walter Verfasser aut Lectures on mathematical logic 2 Calculi for derivations and deductions Walter Felscher Amsterdam Gordon & Breach 2000 X, 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 (DE-604)BV012947413 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008816351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Felscher, Walter Lectures on mathematical logic Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4151278-9 |
| title | Lectures on mathematical logic |
| title_auth | Lectures on mathematical logic |
| title_exact_search | Lectures on mathematical logic |
| title_full | Lectures on mathematical logic 2 Calculi for derivations and deductions Walter Felscher |
| title_fullStr | Lectures on mathematical logic 2 Calculi for derivations and deductions Walter Felscher |
| title_full_unstemmed | Lectures on mathematical logic 2 Calculi for derivations and deductions Walter Felscher |
| title_short | Lectures on mathematical logic |
| title_sort | lectures on mathematical logic calculi for derivations and deductions |
| topic | Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematische Logik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008816351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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