Logic for applications:
Provides an introduction to mathematical logic which is attuned to the applications of logic in computer science. This work emphasizes the notion that deduction is a form of computation. It deals with topics such as resolution theorem proving, logic programming and non-classical logics - modal and i...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1997
|
| Edition: | 2. ed. |
| Series: | Graduate texts in computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Provides an introduction to mathematical logic which is attuned to the applications of logic in computer science. This work emphasizes the notion that deduction is a form of computation. It deals with topics such as resolution theorem proving, logic programming and non-classical logics - modal and intuitionistic. |
| Item Description: | Literaturverz. S. 409 - 438 |
| Physical Description: | XIII, 456 S. |
| ISBN: | 0387948937 |
Staff View
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| 520 | 3 | |a Provides an introduction to mathematical logic which is attuned to the applications of logic in computer science. This work emphasizes the notion that deduction is a form of computation. It deals with topics such as resolution theorem proving, logic programming and non-classical logics - modal and intuitionistic. | |
| 650 | 7 | |a Informatica |2 gtt | |
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| 650 | 7 | |a Wiskundige logica |2 gtt | |
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Record in the Search Index
| _version_ | 1804125807540436992 |
|---|---|
| adam_text | ANIL NERODE RICHARD A. SHORE
LOGIC FOR APPLICATION
S
SECOND EDITION
WITH 78 ILLUSTRATIONS
SPRINGER
CONTENTS
PREFACE V
INTRODUCTIO
N 1
I PROPOSITIONA
L LOGIC 7
1 ORDERS AND TREES 7
2 PROPOSITIONS, CONNECTIVES AND TRUTH TABLES 12
3 TRUTH ASSIGNMENTS AND VALUATIONS 23
4 TABLEAU PROOFS IN PROPOSITIONAL CALCULUS 27
5 SOUNDNESS AND COMPLETENESS OF TABLEAU PROOFS 38
6 DEDUCTIONS FROM PREMISES AND COMPACTNESS 40
7 AN AXIOMATIC APPROACH* 47
8 RESOLUTION 49
9 REFINING RESOLUTION 62
10 LINEAR RESOLUTION, HORN CLAUSES AND PROLOG 66
II PREDICAT
E LOGIC 8
1
1 PREDICATES AND QUANTIFIERS 81
2 THE LANGUAGE: TERMS AND FORMULAS 83
3 FORMATION TREES, STRUCTURES AND LISTS 89
4 SEMANTICS: MEANING AND TRUTH 95
5 INTERPRETATIONS OF PROLOG PROGRAMS 100
6 PROOFS: COMPLETE SYSTEMATIC TABLEAUX 108
7 SOUNDNESS AND COMPLETENESS OF TABLEAU PROOFS 120
8 AN AXIOMATIC APPROACH* 127
CONTENTS
9 PRENEX NORMAL FORM AND SKOLEMIZATION 128
10 HERBRAND S THEOREM 133
11 UNIFICATION 137
12 THE UNIFICATION ALGORITHM 141
13 RESOLUTION 145
14 REFINING RESOLUTION: LINEAR RESOLUTION 153
III
PROLO
G 159
1 SLD-RESOLUTION 159
2 IMPLEMENTATIONS: SEARCHING AND BACKTRACKING 166
3 CONTROLLING THE IMPLEMENTATION: CUT 178
4 TERMINATION CONDITIONS FOR PROLOG PROGRAMS 182
5 EQUALITY 188
6 NEGATION AS FAILURE 192
7 NEGATION AND NONMONOTONIC LOGIC 203
8 COMPUTABILITY AND UNDECIDABILITY 211
I
V MODA
L LOGIC 221
1 POSSIBILITY AND NECESSITY; KNOWLEDGE OR BELIEF 221
2 FRAMES AND FORCING 224
3 MODAL TABLEAUX 228
4 SOUNDNESS AND COMPLETENESS 239
5 MODAL AXIOMS AND SPECIAL ACCESSIBILITY RELATIONS 249
6 AN AXIOMATIC APPROACH* 259
V INTUITIONISTI
C LOGIC 26
3
1
INTUITIONISM AND CONSTRUCTIVISM 263
2 FRAMES AND FORCING 265
3 INTUITIONISTIC TABLEAUX 275
4 SOUNDNESS AND COMPLETENESS 285
5 DECIDABILITY AND UNDECIDABILITY 293
6 A COMPARATIVE GUIDE 306
CONTENTS XIII
V
I ELEMENT
S OF SET THEOR
Y 31
5
1 SOME BASIC AXIOMS OF SET THEORY 315
2 BOOLE S ALGEBRA OF SETS 318
3 RELATIONS, FUNCTIONS AND TH
E POWER SET AXIOM 321
4 THE NATURAL NUMBERS, ARITHMETIC AND INFINITY 328
5 REPLACEMENT, CHOICE AND FOUNDATION 339
6 ZERMELO-FRAENKEL SET THEORY IN PREDICATE LOGIC 345
7 CARDINALITY: FINITE AND COUNTABLE 348
8 ORDINAL NUMBERS 354
9 ORDINAL ARITHMETIC AND TRANSFINITE INDUCTION 360
10 TRANSFINITE RECURSION, CHOICE AND TH
E RANKED UNIVERSE 364
11 CARDINALS AND CARDINAL ARITHMETIC , 368
APPENDI
X A: A
N HISTORICA
L OVERVIE
W 37
5
1 CALCULUS 375
2 LOGIC 376
3 LEIBNIZ S DREAM 379
4 NINETEENTH CENTURY LOGIC 380
5 NINETEENTH CENTURY FOUNDATIONS OF MATHEMATICS 383
6 TWENTIETH CENTURY FOUNDATIONS OF MATHEMATICS 387
7 EARLY TWENTIETH CENTURY LOGIC 389
8 DEDUCTION AND COMPUTATION 392
9 RECENT AUTOMATION OF LOGIC AND PROLO
G 395
10 THE FUTURE 395
APPENDI
X B
: A GENEALOGICA
L DATABAS
E 39
9
BIBLIOGRAPH
Y 40
9
INDE
X O
F SYMBOL
S 43
9
INDE
X OF TERMS 44
3
|
| any_adam_object | 1 |
| author | Nerode, Anil 1932- Shore, Richard A. |
| author_GND | (DE-588)119133865 |
| author_facet | Nerode, Anil 1932- Shore, Richard A. |
| author_role | aut aut |
| author_sort | Nerode, Anil 1932- |
| author_variant | a n an r a s ra ras |
| building | Verbundindex |
| bvnumber | BV011300366 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.9.M35N47 1997 |
| callnumber-search | QA76.9.M35N47 1997 |
| callnumber-sort | QA 276.9 M35 N47 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 ST 120 ST 125 |
| classification_tum | DAT 540f DAT 706f MAT 030f |
| ctrlnum | (OCoLC)35397903 (DE-599)BVBBV011300366 |
| dewey-full | 005.1/01/511320 005.1/01/5113 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.1/01/5113 20 005.1/01/5113 |
| dewey-search | 005.1/01/5113 20 005.1/01/5113 |
| dewey-sort | 15.1 11 45113 220 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:07:26Z |
| institution | BVB |
| isbn | 0387948937 |
| language | German |
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| spelling | Nerode, Anil 1932- Verfasser (DE-588)119133865 aut Logic for applications Anil Nerode ; Richard A. Shore 2. ed. New York [u.a.] Springer 1997 XIII, 456 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in computer science Literaturverz. S. 409 - 438 Provides an introduction to mathematical logic which is attuned to the applications of logic in computer science. This work emphasizes the notion that deduction is a form of computation. It deals with topics such as resolution theorem proving, logic programming and non-classical logics - modal and intuitionistic. Informatica gtt Informatique - Mathématiques ram Logica matematica (textos introdutorios) larpcal Logique symbolique et mathématiques ram Symbolische logica gtt Wiskundige logica gtt Informatik Mathematik Computer science -- Mathematics Logic, Symbolic and mathematical Logische Programmierung (DE-588)4195096-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Logische Programmierung (DE-588)4195096-3 s DE-604 Mathematische Logik (DE-588)4037951-6 s Shore, Richard A. Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590748&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nerode, Anil 1932- Shore, Richard A. Logic for applications Informatica gtt Informatique - Mathématiques ram Logica matematica (textos introdutorios) larpcal Logique symbolique et mathématiques ram Symbolische logica gtt Wiskundige logica gtt Informatik Mathematik Computer science -- Mathematics Logic, Symbolic and mathematical Logische Programmierung (DE-588)4195096-3 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4195096-3 (DE-588)4037951-6 |
| title | Logic for applications |
| title_auth | Logic for applications |
| title_exact_search | Logic for applications |
| title_full | Logic for applications Anil Nerode ; Richard A. Shore |
| title_fullStr | Logic for applications Anil Nerode ; Richard A. Shore |
| title_full_unstemmed | Logic for applications Anil Nerode ; Richard A. Shore |
| title_short | Logic for applications |
| title_sort | logic for applications |
| topic | Informatica gtt Informatique - Mathématiques ram Logica matematica (textos introdutorios) larpcal Logique symbolique et mathématiques ram Symbolische logica gtt Wiskundige logica gtt Informatik Mathematik Computer science -- Mathematics Logic, Symbolic and mathematical Logische Programmierung (DE-588)4195096-3 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Informatica Informatique - Mathématiques Logica matematica (textos introdutorios) Logique symbolique et mathématiques Symbolische logica Wiskundige logica Informatik Mathematik Computer science -- Mathematics Logic, Symbolic and mathematical Logische Programmierung Mathematische Logik |
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