Mathematical structures in language:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stanford, California
CSLI Publications
[2016]
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| Series: | CSLI lecture notes
No. 218 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 473 Seiten Diagramme |
| ISBN: | 9781575868721 9781575868479 |
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Record in the Search Index
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| adam_text | Titel: Mathematical structures in language
Autor: Keenan, Edward L
Jahr: 2016
CSU Lecture Notes No. 218 Mathematical Structures in Language Edward L. Keenan Lawrence S. Moss PUBLICATIONS Center for the Study of Language and Information Stanford, California
Contents Preface ix 1 The Roots of Infinity 1 1.1 The Roots of Infinity in Natural Language........ 2 1.2 Boolean Compounding................... 23 1.3 References.......................... 25 2 Some Mathematical Background 27 2.1 More about Sets ...................... 27 2.2 Sequences.......................... 34 2.3 Functions and Sequences.................. 40 2.4 Arbitrary Unions and Intersections............ 42 2.5 Definitions by Closure (Recursion)............ 43 2.6 Bijections and the Sizes of Cross Products........ 47 2.7 A Linguistic Function................... 50 2.8 A Closing Reflection on Functions ............ 52 2.9 Suggestions for Further Study............... 53 2.10 Addendum 1: Russell’s Paradox.............. 53 2.11 Addendum 2: An Equivalent, Useful, Definition of Closure 54 2.12 Addendum 3: Some Initial Hints on Setting up Proofs . 56 3 Boolean Phonology 61 3.1 Abstract Segmental Phonology.............. 63 3.2 Enriching Feature Sets................... 68 3.3 Some Phonological Generalizations............ 69 3.4 The Mathematical Structure of Feature Sets....... 71 3.5 Significant Sound Segments................ 72
vi / Mathematical Structures in Language 4 Syntax I: Trees and Order Relations 81 4.1 Trees............................. 82 4.2 C-Command ........................ 95 4.3 Sameness of Structure: Isomorphism........... 99 4.4 Labeled Trees........................105 4.5 Ordered Trees........................110 4.6 Concluding Formal Exercises on Relations and Ordered Trees.............................121 5 Syntax II: Design for a Language 129 5.1 Beginning Grammar....................130 5.2 Eng- Towards a Grammar of English..........132 5.3 Word Order Variation in Other Languages........137 5.4 Three New Types of DPs .................139 6 A Taste of Formal Language Theory 147 6.1 Introduction.........................147 6.2 CFGs: A Formal Definition................149 6.3 How Well Do CFGs Model Natural Languages?.....158 7 Finite State Automata 183 7.1 Finite-State Automata...................184 7.2 Regular Expressions and Languages ...........191 7.3 Simple Grammars .....................197 7.4 Closing the Circle......................201 7.5 a n b n is not a Regular Language..............206 7.6 An Argument Why English is Not Regular........208 7.7 Two Final Observations on Finite State Automata . . . 209 8 Semantics I: Compositionality and Sentential Logic 215 8.1 Compositionality and Natural Language Semantics . . . 215 8.2 Sentential Logic.......................225 8.3 Interpreting a Fragment of English............239 9 Semantics II: Coordination, Negation and Lattices 257 9.1 Coordination: Syntax ...................259 9.2 Coordination: Semantics..................260 9.3 Negation and Additional Properties of Natural Language Lattices...........................270 9.4 Properties versus Sets: Lattice Isomorphisms......275 9.5 Theorems on Boolean Lattices ..............279 9.6 Some (Possibly) Unexpected Boolean Lattices......280
Contents / vii 9.7 A Concluding Note on Point of View...........281 9.8 Further Reading ......................283 9.9 Appendix: Tarski-Knaster and Schröder-Bernstein . . . 283 10 Semantics III: Logic and Variable Binding Operators 285 10.1 Translation Semantics...................285 10.2 Some General Linguistic Properties of First Order Logic (FOL)............................304 10.3 Extending the Class of VBO’s: The Lambda Operator . 316 11 Semantics IV: DPs, Monotonicity and Semantic Generalizations 335 11.1 Negative Polarity Items..................335 11.2 Monotonicity........................340 11.3 Semantic Generalizations .................348 11.4 Historical Background...................353 12 Semantics V: Classifying Quantifiers 357 12.1 Quantifier Types......................359 12.2 Generalizations Concerning Det Denotations ......370 12.3 fc-Place Dets ........................375 12.4 Crossing the Frege Boundary...............379 12.5 A Classic Syntactic Problem................381 12.6 Adverbial Quantification..................383 12.7 Concluding Remarks....................387 12.8 Historical Background...................388 12.9 Appendix: Some Types of English Determiners.....388 13 Linguistic Invariants 391 13.1 A Model Grammar and Some Basic Theorems......393 13.2 A Semantic Definition of Anaphor ............407 13.3 A Model of Korean.....................411 13.4 Toba Batak.........................416 13.5 Some Mathematical Properties of Grammars and their Invariants..........................420 13.6 Invariants of Type 0....................422 13.7 Invariants of Type (1)...................423 13.8 Invariants of Type (2) and Higher ............426 13.9 Structure Preserving Operations on Grammars.....431 List of Symbols 435 The Greek Alphabet.......................435
viii / Mathematical Structures in Language Bibliography 437 Author Index 457 Language Index 463 Subject Index 465
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| spelling | Keenan, Edward L. 1937- Verfasser (DE-588)13756211X aut Mathematical structures in language Edward L. Keenan & Lawrence S. Moss Stanford, California CSLI Publications [2016] xi, 473 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier CSLI lecture notes No. 218 Mathematical linguistics Mathematische Linguistik (DE-588)4037950-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Linguistik (DE-588)4037950-4 s DE-604 Moss, Lawrence Stuart 1959- Verfasser (DE-588)133971589 aut CSLI lecture notes No. 218 (DE-604)BV001900711 218 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028699395&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keenan, Edward L. 1937- Moss, Lawrence Stuart 1959- Mathematical structures in language CSLI lecture notes Mathematical linguistics Mathematische Linguistik (DE-588)4037950-4 gnd |
| subject_GND | (DE-588)4037950-4 (DE-588)4123623-3 |
| title | Mathematical structures in language |
| title_auth | Mathematical structures in language |
| title_exact_search | Mathematical structures in language |
| title_full | Mathematical structures in language Edward L. Keenan & Lawrence S. Moss |
| title_fullStr | Mathematical structures in language Edward L. Keenan & Lawrence S. Moss |
| title_full_unstemmed | Mathematical structures in language Edward L. Keenan & Lawrence S. Moss |
| title_short | Mathematical structures in language |
| title_sort | mathematical structures in language |
| topic | Mathematical linguistics Mathematische Linguistik (DE-588)4037950-4 gnd |
| topic_facet | Mathematical linguistics Mathematische Linguistik Lehrbuch |
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