Introduction to mathematical linguistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice-Hall
1972
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 337 S. Ill. |
| ISBN: | 013487496X |
Staff View
MARC
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| 100 | 1 | |a Wall, Robert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to mathematical linguistics |c Robert Wall |
| 264 | 1 | |a Englewood Cliffs, NJ |b Prentice-Hall |c 1972 | |
| 300 | |a XIV, 337 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Matematisk lingvistik |2 KBslagord | |
| 650 | 4 | |a Mathematical linguistics | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiü
1 Elements of Set Theory 1
Specification of Sets, 2
Equality of Sets: The Axiom of Extension, 4
Sets of Sets, 6
Subsets, 6
Members vs. Subsets, 7
Power Sets, 8
Exercises, 7
References and Supplementary Reading, 10
2 Symbolic Logic:
The Propositional Calculus 12
Propositions, 13
The Logical Connectives, 15
1. Conjunction, 15
2. Disjunction, 16
3. Negation, 17
4. The Conditional, 18
5. The Biconditional, 21
More Complex Propositions, 22
Tautologies and Contradictions, 25
Logical Equivalence, 27
Arguments, 34
vii
viii Contents
Validity and Truth, 37
Rules of Inference, 38
Conditional Proof, 41
Indirect Proof, 44
Exercises, 45
3 The Predicate Calculus 51
Terms, Predicates, Propositional Functions, 52
Quantifiers, 53
Bound and Free Variables, 56
The Domain of Discourse, 57
Set Specification and Predicates, 58
Representation of Universal and
Existential Statements, 59
Tautology, Contradiction, and Logical Equivalence, 62
Arguments Involving Quantifiers, 65
1. Universal Instantiation, 65
2. Universal Generalization, 66
3. Existential Generalization, 68
4. Existential Instantiation, 68
Conditional Proof in the Predicate Calculus, 71
Arguments Containing Propositions
with Two or More Quantifiers, 73
Exercises, 76
References and Supplementary Reading, 80
4 Further Aspects of Set Theory 81
Some Set-Theoretic Predicates, 81
Some Theorems about Sets, 83
Informal Style in Mathematical Proofs, 84
Set Operations, 87
1. Union, 87
2. Intersection, 89
3. Relative Complementation, 91
4. Absolute Complementation, 92
Venn Diagrams, 92
Set-Theoretic Equalities, 98
Exercises, 102
5 Ordered Pairs, Cartesian Products,
Relations, and Functions 104
Ordered Pairs, 104
Cartesian Products, 106
Relations, 107
Contents ix
Domain and Range of a Relation, 108
Universal, Null, and Identity Relations, 109
Complementary and Inverse Relations, 109
Properties of Relations, 110
1. Reflexivity, 110
2. Symmetry, 111
3. Transitivity, 113
4. Connexity, 114
Diagrams of Relations, 115
Properties of Complementary
and Inverse Relations, 117
Equivalence Relations and Partitions, 121
Functions, 124
Inverse Functions, 127
Composites, 129
Identity Functions, 130
Inverses of Composites, 131
Exercises, 133
6 Orders, Operation.?, Configurations,
and Isomorphisms 137
Orders, 137
Terminology, 140
Trees, 144
1. Dominance, 145
2. Precedence, 147
3. Labeling, 148
Operations, 152
Properties of Operations, 153
1. Well-definition, 153
2. Closure, 154
3. Associativity, 154
4. Commutativity, 154
5. Idempotence, 154
6. Distributivity, 155
7. Identity Elements, 155
8. Inverse Elements, 156
9. Zero Elements, 157
Mathematical Configurations
Involving Operations, 157
1. Groups, 158
2. Subgroups, 160
3. Monoids, 162
4. Submonoids, 163
5. Semigroups, 163
Strings, 164
Isomorphisms, 166
Exercises, 172
X Contents
7 Infinite Sets 174
Equivalent Sets and Cardinality, 174
Denumerability of Sets, 177
Nondenumerable Sets, 181
Exercises, 186
References and Supplementary Reading, 186
8 Recursion 188
Recursive Definition, 188
Induction, 193
Axiomatic Systems, 197
Extended Axiomatic Systems, 199
Semi-Thue Systems, 202
Exercises, 204
References and Supplementary Reading, 206
9 Grammars of Formal Languages 207
Formal Grammars, 207
Types of Grammars, 211
Types of Languages, 213
Grammars and Constituent-Structure Trees, 214
Right-Linear Grammars and Languages, 221
1. An Equivalent Formulation of Right-Linear Grammars, 223
2. Type 3 Languages and Regulär Sets, 225
3. Inadequacy of Right-Linear Grammars for Natural
Languages, 231
Context-Sensitive Grammars and Languages, 234
1. Existence of a Decision Procedure for Membership in a Type 1
Language, TiA
2. Type 1 Languages and Recursive Sets, 236
3. Some Undecidable Questions Concerning Type 1 Grammars and
Languages, 238
Context-Free Grammars and Languages, 238
1. Decidability of the Emptiness Question for Context-Free
Grammars, 239
2. Reductions of Context-Free Grammars, 241
3. A Characterization Theorem for Context-Free Languages, 247
4. Closure Properties of Context-Free Languages, 249
Exercises, 251
References and Supplementary Reading, 252
10 Automata 254
Finite Automata, 254
1. State Diagrams of Finite Automata, 257
2. Deterministic vs. Nondeterministic Finite Automata, 258
Contents xi
3. Formal Definition of Deterministic Finite Automata, 259
4. Finite Automata and Type 3 Grammars, 261
5. Finite Automata as Generators, 264
6. Finite Automata and Regulär Sets, 265
7. Finite Automata and Equivalence Relations, 267
Turing Machines, 274
1. Formal Definition of Turing Machines, 276
2. Equivalent Formulations of Turing Machines, 278
3. Recursive vs. Recursively Enumerable Sets, 279
4. Equivalence of Turing Machines and Type 0 Grammars, 280
Pushdown Automata, 282
Linear-Bounded Automata, 285
Exercises, 287
References and Supplementary Reading, 288
11 Mathematical Characterization
of Transformational Grammars 289
References and Supplementary Reading, 296
Bibliography 298
Answers to Selected Exercises 304
Index of Symbols 321
General Index 323
|
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| dewey-hundreds | 400 - Language |
| dewey-ones | 410 - Linguistics |
| dewey-raw | 410 |
| dewey-search | 410 |
| dewey-sort | 3410 |
| dewey-tens | 410 - Linguistics |
| discipline | Sprachwissenschaft Philosophie Literaturwissenschaft |
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| institution | BVB |
| isbn | 013487496X |
| language | English |
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| physical | XIV, 337 S. Ill. |
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| spelling | Wall, Robert Verfasser aut Introduction to mathematical linguistics Robert Wall Englewood Cliffs, NJ Prentice-Hall 1972 XIV, 337 S. Ill. txt rdacontent n rdamedia nc rdacarrier Matematisk lingvistik KBslagord Mathematical linguistics Mathematische Linguistik (DE-588)4037950-4 gnd rswk-swf Mathematische Linguistik (DE-588)4037950-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001959662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wall, Robert Introduction to mathematical linguistics Matematisk lingvistik KBslagord Mathematical linguistics Mathematische Linguistik (DE-588)4037950-4 gnd |
| subject_GND | (DE-588)4037950-4 |
| title | Introduction to mathematical linguistics |
| title_auth | Introduction to mathematical linguistics |
| title_exact_search | Introduction to mathematical linguistics |
| title_full | Introduction to mathematical linguistics Robert Wall |
| title_fullStr | Introduction to mathematical linguistics Robert Wall |
| title_full_unstemmed | Introduction to mathematical linguistics Robert Wall |
| title_short | Introduction to mathematical linguistics |
| title_sort | introduction to mathematical linguistics |
| topic | Matematisk lingvistik KBslagord Mathematical linguistics Mathematische Linguistik (DE-588)4037950-4 gnd |
| topic_facet | Matematisk lingvistik Mathematical linguistics Mathematische Linguistik |
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