The logic of categorial grammars: a deductive account of natural language syntax and semantics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schriftenreihe: | Lecture notes in computer science
6850 : Tutorial |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVIII, 302 S. graph. Darst. |
| ISBN: | 3642315542 9783642315541 |
Internformat
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| 245 | 1 | 0 | |a The logic of categorial grammars |b a deductive account of natural language syntax and semantics |c Richard Moot ; Christian Retoré |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
PREFACE VII
REFERENCES XIII
1 CLASSICAL CATEGORIAL GRAMMARS: AB GRAMMARS 1
1.1 SEMANTIC CATEGORIES AND AJDUKIEWICZ FRACTIONS 1
1.2 CLASSICAL CATEGORIAL GRAMMARS OR AB GRAMMARS 2
1.3 AB GRAMMARS AND CONTEXT-FREE GRAMMARS 6
1.3.1 CONTEXT-FREE GRAMMARS 6
1.3.2 FROM CONTEXT-FREE GRAMMARS TO AB GRAMMARS 7
1.3.3 FROM AB GRAMMARS TO CONTEXT-FREE GRAMMARS 8
1.4 PARSING AB GRAMMARS 8
1.5 LIMITATIONS O F AB GRAMMARS 9
1.6 LEARNING AB GRAMMARS 9
1.6.1 GRAMMATICAL INFERENCE FOR CATEGORIAL GRAMMARS 10
1.6.2 UNIFICATION AND AB GRAMMARS 10
1.6.3 THE RG ALGORITHM 11
1.6.4 OTHER CASES 15
1.7 CONCLUDING REMARKS 16
EXERCISES FOR CHAPTER 1 18
REFERENCES 21
2 A LOGIC FOR CATEGORIAL GRAMMARS: LAMBEK'S SYNTACTIC CALCULUS . . . .
23 2.1 LAMBEK'S SYNTACTIC CALCULUS AND LAMBEK GRAMMARS 23
2.2 NATURAL DEDUCTION FOR THE LAMBEK CALCULUS 24
2.2.1 IN PRAWITZ STYLE 24
2.2.2 IN GENTZEN STYLE 27
2.3 SEQUENT CALCULUS 28
2.4 EQUIVALENCE O F SEQUENT CALCULUS AND NATURAL DEDUCTION 31
2.4.1 FROM NATURAL DEDUCTION TO SEQUENT CALCULUS 31
2.4.2 FROM SEQUENT CALCULUS TO NATURAL DEDUCTION 31
2.5 THE EMPTY SEQUENCE 33
2.6 NORMALIZATION OF NATURAL DEDUCTION 33
HTTP://D-NB.INFO/1023016486
IMAGE 2
X V I C O N T E N T S
2.6.1 NORMALIZATION FOR THE PRODUCT-FREE LAMBEK CALCULUS 34
2.6.2 DECIDABILITY OF NATURAL DEDUCTION 37
2.6.3 NORMALIZATION AND LAMBEK CALCULUS WITH PRODUCT 39
2.7 CUT-ELIMINATION FOR THE SEQUENT CALCULUS 39
2.8 DECIDABILITY 4 3
2.9 MODELS FOR THE LAMBEK CALCULUS AND COMPLETENESS 44
2.9.1 RESIDUATED SEMI-GROUPS 44
2.9.2 THE FREE GROUP MODEL 45
2.9.3 L IS SOUND AND COMPLETE W.R.T. RESIDUATED SEMI-GROUPS . . . 4 6
2.9.4 L IS SOUND AND COMPLETE W.R.T. (FREE) SEMI-GROUP MODELS 47
2.10 INTERPOLATION 48
2.11 LAMBEK GRAMMARS AND CONTEXT-FREE GRAMMARS 52
2.11.1 FROM CONTEXT-FREE GRAMMARS TO LAMBEK GRAMMARS 53 2.11.2 A
PROPERTY O F THE FREE GROUP 53
2.11.3 INTERPOLATION FOR THIN SEQUENTS 55
2.1 1.4 FROM LAMBEK GRAMMARS TO CONTEXT-FREE GRAMMARS 57 2.12 CONCLUDING
REMARKS 58
EXERCISES FOR CHAPTER 2 6 0
REFERENCES 62
3 LAMBEK CALCULUS AND MONTAGUE GRAMMAR 65
3.1 INTRODUCTION 65
3.2 LOGIC AND LAMBDA CALCULUS 66
3.2.1 TYPED LAMBDA CALCULUS AND INTUITIONISTIC PROPOSITIONAL CALCULUS 66
3.2.2 FIRST ORDER LOGIC, MONO AND MULTISORTED 69
3.2.3 SECOND ORDER AND HIGHER ORDER LOGIC 71
3.2.4 LAMBDA TERMS AND LOGICAL FORMULAE 72
3.3 FROM CATEGORIAL ANALYSIS TO MONTAGUE SEMANTIC ANALYSIS 74
3.4 SOME TYPICAL EXAMPLES 76
3.5 DETERMINERS, QUANTIFIERS AND TYPE RAISING 84
3.6 LAMBEK CALCULUS AND DISCOURSE REPRESENTATION THEORY 86
3.7 A WORD ABOUT INTENSIONAL LOGIC 93
3.8 CONCLUDING REMARKS 95
EXERCISES FOR CHAPTER 3 96
REFERENCES 98
4 THE NON-ASSOCIATIVE LAMBEK CALCULUS 101
4.1 INTRODUCTION 101
4.2 PROOF THEORY 102
4.2.1 SEQUENT CALCULUS 103
4.2.2 ARGUMENTS AGAINST ASSOCIATIVITY 105
4.2.3 CUT ELIMINATION FOR THE NL SEQUENT CALCULUS 107
4.2.4 NATURAL DEDUCTION 110
IMAGE 3
CONTENTS XVII
4.3 STRUCTURAL RULES I L L
4.4 COMBINATOR CALCULI FOR NL 113
4.4.1 ALTERNATIVE AXIOMATIC PRESENTATIONS 114
4.4.2 EQUIVALENCE BETWEEN THE AXIOMATIC REPRESENTATION AND SEQUENT
CALCULUS 116
4.5 MODEL THEORY 120
4.5.1 SOUNDNESS AND COMPLETENESS 122
4.5.2 ADDING STRUCTURAL RULES 126
4.6 POLYNOMIAL COMPLEXITY 129
4.6.1 COMPLEXITY 129
4.6.2 DE GROOTE'S CONTEXT CALCULUS SC 130
4.6.3 A THEOREM PROVING ALGORITHM 139
4.6.4 NL WITHOUT PRODUCT 140
4.7 CONCLUDING REMARKS 143
EXERCISES FOR CHAPTER 4 144
REFERENCES 147
5 THE MULTIMODAL LAMBEK CALCULUS 1 49
5.1 COMBINING DIFFERENT CALCULI 149
5.1.1 MULTIMODAL STRUCTURAL RULES 151
5.2 UNARY CONNECTIVES 160
5.2.1 THE UNARY CONNECTIVES OF LINEAR LOGIC 160
5.2.2 UNARY RESIDUATION 162
5.2.3 STRUCTURAL RULES 165
5.2.4 THE GENERAL FORM O F STRUCTURAL RULES 170
5.2.5 CUT ELIMINATION 172
5.3 NATURAL DEDUCTION 175
5.4 AXIOMATIC PRESENTATION 178
5.5 MODEL THEORY 180
5.5.1 COMPLETENESS FOR WEAK SAHLQVIST POSTULATES 183
5.6 CONCLUDING REMARKS 184
EXERCISES FOR CHAPTER 5 185
REFERENCES 190
6 LAMBEK CALCULUS AND LINEAR LOGIC: PROOF NETS AS PARSE STRUCTURES 193
6.1 THE FORMULA LANGUAGE O F CATEGORIAL GRAMMAR AND OF LINEAR LOGIC 193
6.1.1 THE FORMULA LANGUAGE O F MULTIPLICATIVE LINEAR LOGIC 193 6.1.2
REDUCED LINEAR LANGUAGE (NEGATIVE NORMAL FORM) 195 6.1.3 RELATING
CATEGORIES AND LINEAR LOGIC FORMULAE: POLARITIES 195
6.2 TWO SIDED CALCULI 197
6.2.1 PROPERTIES O F THE LINEAR TWO SIDED SEQUENT CALCULUS 197 6.2.2 THE
INTUITIONISTIC TWO SIDED CALCULUS LP 199
6.2.3 PROOFS AS PARSE STRUCTURES: TOO MANY O F THEM 201
IMAGE 4
X V I I I C O N T E N T S
6.3 A ONE SIDED CALCULUS FOR LINEAR LOGIC: MLL 201
6.3.1 VARIANTS 202
6.3.2 THE INTUITIONISTIC RESTRICTION IN ONE SIDED CALCULI 203
6.4 PROOF NETS: CONCISE AND EXPRESSIVE PROOFS 206
6.4.1 PROOF NETS FOR MLL 207
6.4.2 SEQUENT CALCULUS AND PROOF NETS 211
6.4.3 INTUITIONISTIC PROOF NETS 214
6.4.4 CYCLIC PROOF NETS 215
6.4.5 PROOF NETS FOR THE LAMBEK CALCULUS - WITH OR WITHOUT EMPTY
ANTECEDENT 218
6.4.6 CUT ELIMINATION FOR PROOF NETS 221
6.4.7 CUTS AND NON-COMMUTATIVE PROOF NETS 223
6.4.8 BASIC PROPERTIES OF GRAPHS AND PROOF NETS 225
6.5 PARSING AS PROOF NET CONSTRUCTION 227
6.6 PROOF NETS AND HUMAN PROCESSING 229
6.7 SEMANTIC USES OF PROOF NETS 231
6.8 CONCLUDING REMARKS 233
EXERCISES FOR CHAPTER 6 234
REFERENCES 236
7 PROOF NETS FOR THE MULTIMODAL LAMBEK CALCULUS: FROM THEORY TO A
WIDE-COVERAGE CATEGORIAL PARSER 239
7.1 MULTIMODAL PROOF NETS 239
7.1.1 TWO SIDED PROOF NETS 240
7.1.2 MULTIMODAL PROOF STRUCTURES AND ABSTRACT PROOF STRUCTURES 245
7.1.3 PROOF NETS AND CONTRACTIONS 255
7.1.4 SEQUENT CALCULUS AND MULTIMODAL PROOF NETS 262
7.2 GRAIL: PARSING WITH MULTIMODAL PROOF NETS 271
7.2.1 INTERACTIVE PARSING 272
7.2.2 PRUNING THE SEARCH SPACE 279
7.2.3 WIDE-COVERAGE PARSING 283
7.3 CONCLUDING REMARKS 293
EXERCISES FOR CHAPTER 7 294
REFERENCES 296
INDEX 299 |
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| indexdate | 2025-01-10T15:15:13Z |
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| isbn | 3642315542 9783642315541 |
| language | English |
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| physical | XVIII, 302 S. graph. Darst. |
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| publisher | Springer |
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| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science FoLLI publications on logic, language and information |
| spelling | Moot, Richard Verfasser aut The logic of categorial grammars a deductive account of natural language syntax and semantics Richard Moot ; Christian Retoré Berlin [u.a.] Springer 2012 XVIII, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 6850 : Tutorial FoLLI publications on logic, language and information Kategorialgrammatik (DE-588)4263781-8 gnd rswk-swf Natürliche Sprache (DE-588)4041354-8 gnd rswk-swf Lambek-Kalkül (DE-588)4737091-9 gnd rswk-swf Computerlinguistik (DE-588)4035843-4 gnd rswk-swf Natürliche Sprache (DE-588)4041354-8 s Kategorialgrammatik (DE-588)4263781-8 s Lambek-Kalkül (DE-588)4737091-9 s Computerlinguistik (DE-588)4035843-4 s DE-604 Retoré, Christian Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-31555-8 Lecture notes in computer science 6850 : Tutorial (DE-604)BV000000607 6850 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4052439&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025264475&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moot, Richard Retoré, Christian The logic of categorial grammars a deductive account of natural language syntax and semantics Lecture notes in computer science Kategorialgrammatik (DE-588)4263781-8 gnd Natürliche Sprache (DE-588)4041354-8 gnd Lambek-Kalkül (DE-588)4737091-9 gnd Computerlinguistik (DE-588)4035843-4 gnd |
| subject_GND | (DE-588)4263781-8 (DE-588)4041354-8 (DE-588)4737091-9 (DE-588)4035843-4 |
| title | The logic of categorial grammars a deductive account of natural language syntax and semantics |
| title_auth | The logic of categorial grammars a deductive account of natural language syntax and semantics |
| title_exact_search | The logic of categorial grammars a deductive account of natural language syntax and semantics |
| title_full | The logic of categorial grammars a deductive account of natural language syntax and semantics Richard Moot ; Christian Retoré |
| title_fullStr | The logic of categorial grammars a deductive account of natural language syntax and semantics Richard Moot ; Christian Retoré |
| title_full_unstemmed | The logic of categorial grammars a deductive account of natural language syntax and semantics Richard Moot ; Christian Retoré |
| title_short | The logic of categorial grammars |
| title_sort | the logic of categorial grammars a deductive account of natural language syntax and semantics |
| title_sub | a deductive account of natural language syntax and semantics |
| topic | Kategorialgrammatik (DE-588)4263781-8 gnd Natürliche Sprache (DE-588)4041354-8 gnd Lambek-Kalkül (DE-588)4737091-9 gnd Computerlinguistik (DE-588)4035843-4 gnd |
| topic_facet | Kategorialgrammatik Natürliche Sprache Lambek-Kalkül Computerlinguistik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4052439&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=025264475&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000607 |
| work_keys_str_mv | AT mootrichard thelogicofcategorialgrammarsadeductiveaccountofnaturallanguagesyntaxandsemantics AT retorechristian thelogicofcategorialgrammarsadeductiveaccountofnaturallanguagesyntaxandsemantics |