Current Issues in Mathematical Linguistics (eBook)

Front Cover 1
Current Issues in Mathematical Linguistics 4
Copyright Page 5
Table of Contents 16
Preface 6
LIST OF COMMITTEES 8
INTRODUCTION 11
I. General mathematical models 11
III. Lexical, Formal Semantics and Discursive Models 12
IV. Applications in Natural Language Processing 13
PART 1: GENERAL MATHEMATICAL MODELS 20
CHAPTER 1. THE STATUS OF RESEARCH IN THE FIELD OF ANALYTICALA L GEBRAIC MODELS OF LANGUAGE 22
1. INTRODUCTION. ANALYTIC VERSUS GENERATIVE 22
2 . PHONOLOGY AND SEGMENTATION 24
3 . DOMINATION RELATIONS 26
4. CLOSURE OPERATORS AND GALOIS CONNECTIONS 29
5. PARTS OF SPEECH, GENDER, CASE, LINGUISTIC TYPOLOGY 31
6. THE CONTEXTUAL SPACE TOPOLOGY
REFERENCES 34
CHAPTER 2. ON GALOIS CONNEXIONS 42
1. INTRODUCTION 42
2. PROPERTIES OF THE OPERATORS G, ù AND Ø 43
REFERENCES 46
Chapter 3. A Model of Anaphora Resolution Based on Distributional-AlgebraicApproach in Analytical Models Theory of Algebraic Linguistics 48
1. INTRODUCTION 48
2. DISTRIBUTIONAL - ALGEBRAIC TECHNIQUES IN ANALYTICALMODELS THEORY OF ALGEBRAIC LINGUISTICS 48
3. ANAPHORIC PAIRS AND PARADIGMATIC SEQUENCES OFQUASI-ANAPHORS 50
4. IDENTIFYING STRINGS, TEXTUAL SEMANTICS 50
5. SEMANTICS. PRUNING. THE ANAPHORIC TREE 51
6. FOCUSING 53
7. THE GENERAL SCHEME OF FOCUSING 54
8. CONCLUSIONS 55
REFERENCES 56
Chapter 4. Anaphoric instantiation problems in an inferential model of utterancerepresentation 58
1. GRAMMAR AS A LABELLED DEDUCTIVE SYSTEM 58
2. DATABASES AND MODEL SETS 60
3. ANAPHORA AND EXISTENTIAL PRESUPPOSITIONS 61
REFERENCES 67
Chapter 5. A formal approach to nominalization of predicates 68
1. INTRODUCTION 68
2. FORMAL LANGUAGE 69
3. SEMANTICS 70
4. NORMAL MODELS 75
REFERENCES 77
Chapter 6. Nominalization in Locally Standard Grammar 78
1. Locally Standard Grammar 78
2. Quasi-Truth 79
3. Quasi-Propositions 80
4. Nominalization and Propositional Attitudes 83
5. On the Syntactic Treatment of Modality 85
References 87
Chapter 7. Topological linguistics and the study of linguistic variation 88
1. THE PROBLEM OF LINGUISTIC VARIATION 88
2. VARIATION IN TOPOLOGICAL LINGUISTICS 90
3. TYPES OF VARIATION 91
REFERENCES 95
Chapter 8. Semantic Space Model and Linguistic Inadequacy 98
1. MATERIAL OBJECTS 98
2. MENTAL ENTITIES 98
3. SPEECH AND THOUGHT 100
4. CARDINALITIES 102
5. INADEQUACY 103
REFERENCES 103
Chapter 9. How to infer non-formal conclusions from mathematical models in the analysis of natural language: A preliminary case study in communication theory 104
1. ANALOGIES 104
2. STATIC DESCRIPTION OF PRODUCTION/COMMUNICATION 105
3. DYNAMIC DESCRIPTION OF PRODUCTION/COMMUNICATION 106
4. RATIONAL BEHAVIOUR: CHOICE 106
5. AGREEMENT 107
6. EQUILIBRIUM 107
REFERENCES 108
Chapter 10. 
110 
1. BRACKETED GRID THEORY 110
2. AUTOSEGMENTAL REPRESENTATIONS 113
3. BRACKETED GRIDS AS AR'S 116
4. CONCLUSION 119
REFERENCES 119
PART II: FORMAL GRAMMAR MODELS 120
Chapter11. An Overview of Stratified Feature Grammar 122
1. Introduction 122
2. Stratified Feature Structures 123
3. Some Historical Remarks 127
4. The SFG Framework 129
5. Some Formal Properties of SFG 135
6. Concluding Remarks 136
REFERENCES 137
Chapter 12. A Rewriting System for Natural Language Syntax that isNon-Local a n d Mildly Context Sensitive 140
1. MILD CONTEXT-SENSITIVITY AND LOCALITY 140
2. GERMAN SCRAMBLING AND LOCALITY 142
3. A NON-LOCAL SYSTEM 143
4. POLYNOMIAL RECOGNITION 145
5. DISCUSSION 148
REFERENCES 148
Chapter 13. Restricted Discontinuous Phrase Structure Grammar and ItsRamifications 150
1. Introduction 150
2. Definitions 151
3. More Examples 154
4. Application 157
5. Complexity 157
References 159
Chapter 14. Polychrome tree grammars (PTGs): a formal presentation 160
0. INTRODUCTION 160
1. MOTIVATION 160
2. POLYCHROME TREES 162
3. TREE COMPOSITION 164
4. TREE GRAMMARS 166
5. CONTEXT-SENSITIVITY 167
6. CONCLUSION 168
REFERENCES 168
CHAPTER 15. ON THE CHARACTERIZATION OF SOME GENERATIVEGRAMMARS BY NUMERICAL FUNCTIONS 170
1. INTRODUCTION 170
2. THE CHARACTERISTIC-LENGTH FUNCTION 171
3. THE DEPTH FUNCTION 172
4. THE ARC FUNCTION 177
5. THE COMPARISON OF THE FUNCTIONS 178
REFERENCES 179
Chapter 16. Approximation in languages 180
1. THE METRIC ON FORMAL LANGUAGES 180
2. NOTES ON METRICS FOR NATURAL LANGUAGES 182
3. THE APPROXIMATION IN A FORMAL LANGUAGE 184
4. A PROBLEM OF APPROXIMATION IN NATURAL LANGUAGES 186
5. CONCLUSIONS 188
REFERENCES 188
Chapter 17. On some formal properties of coordination 190
1. INTRODUCTION: COORDINATION 190
2. LICENSING OF ADJUNCTS (MODIFIERS) 191
3. ASYMMETRICAL COORDINATION 192
4. HÔHLE GAPS 193
5. CHARACTERISTICS OF ASYMMETRICAL CONSTRUCTIONS 194
6. SUGGESTION 195
7. CONCLUSION 198
REFERENCES 199
Chapter 18. Are Features Inherited? 200
1. INTRODUCTION 200
2. PROBLEMATIC DATA 201
3. INVERSE ELEMENTS VS. MONOTONOUS FAILURE 204
4. GENETIC INHERITANCE 206
5. THE STRUCTURE OF COORDINATION CLAUSES 208
6. CONCLUSIONS AND REMAINING PROBLEMS 209
REFERENCES 209
Chapter 19. A compact syntactic representation 210
1. INTRODUCTION 210
2. THE PARSING ALGORITHM 212
3. STRUCTURE OF THE DEPENDENCY GRAPH 214
4. INDICES AT WORK 217
5. CONCLUSION 218
REFERENCES 219
Chapter 20. Non-finite auxiliaries as affixes 220
Abstract 220
Linguistic observations 220
The problem of "split infinitives" 221
Auxiliaries and other verbs 222
Prolog implementation of affixing rule 222
Addition of the ininitive marker to 223
Placement of affixing rule in a full grammar 223
Other languages 224
Demos 225
Conclusions and discussion 226
Acknowledgement 227
References 227
Chapter 21. Formal description of complex noun phrases with predicative nouns 228
1. INTRODUCTION 228
2. PREDICATIVE NOUN PHRASES 228
3. FORMAL DESCRIPTION 229
4. OBJECT STRINGS 231
5. LEXICAL ENTRIES 235
6. CONCLUSION 237
REFERENCES 237
PART III: LEXICAL, FORMAL SEMANTICSAND DISCURSIVE MODELS 238
Chapter 22. Semantic Typing and Degrees of Polymorphism 240
1. Degrees of Polymorphism 240
2. Strong vs. Weak Compositionality 245
3. The Formal Nature of Generative Devices 247
4. Conclusion 255
REFERENCES 255
Chapter 23. Entailment in logic and in the lexicon 258
1. INTRODUCTION 258
2. THE NOTION OF LINGUISTIC ENTAILMENT 258
3. LINGUISTIC ENTAILMENT AND LANGUAGE SPECIFIC SEMANTICSTRUCTURES 262
4. AN OUTLINE OF A COMPUTATIONAL APPLICATION AND SOMETHEORETICAL CONSEQUENCES 265
REFERENCES 267
Chapter 24. Schematicity in Lexical Representations 268
1. DIFFERENT KINDS OF LEXICAL INFORMATION 268
2. SCHEMATIC STRUCTURES 272
3. CONCLUSION. DIFFERENT TYPES OF INFORMATION 275
REFERENCES 276
CHAPTER 25. THE TIME AND CONCEPTUAL BASIS OF AKTIONSART 278
1. INTRODUCTION 278
2. é WHAT ARE SITUATIONS 278
3. VENDLER-DOWTY PROPOSAL 279
4. THE TEMPORAL STUDY OF SITUATIONS 280
5. CONCEPTUAL CATEGORIZATION OF SITUATIONS 281
6. SYNTAX-SEMANTICS CONNECTIONS 283
7. THE CONNECTIONS BETWEEN TIME AND CONCEPTUAL STRUCTURES:SPANISH PERFECTIVE ADJECTIVE 284
8. FINAL 286
REFERENCES 287
Chapter 26. A Mereological Characterization of Temporal and Aspectual Phenomena 288
1. INTRODUCTION 288
2. THE PRESENT TENSE 288
3. EVENT DOMAINS 289
4. APPLYING THE THEORY 292
REFERENCES 296
Chapter 27. Temporal Information Retrieval from Text 298
1. INTRODUCTION 298
2. THE INTERPRETATION OF SENTENCE'S TENSE AND ASPECT 299
3. REPRESENTING THE TEXT TEMPORAL FACTS 301
4. EXAMPLE 304
5. RELATED WORK AND CONCLUSIONS 305
REFERENCES 306
Chapter 28. Dynamic Interpretation, Negation and VP-Anaphora 308
1. Introduction 308
2. Dynamic Interpretation 309
3. Dynamic Representation and VP-Eliipsis 311
References 317
Chapter 29. BABY-SIT: Towards a situation-theoreticcomputational environment 318
1. INTRODUCTION 318
2. SITUATIONS: A COMPUTATIONAL PERSPECTIVE 319
3. THE PROPOSED COMPUTATIONAL MODEL 320
4. CURRENT VERSION OF BABY-SIT 321
5. CONCLUSIONS 325
REFERENCES 327
CHAPTER 30. SOME METALOGICAL CONSTRAINTS ON FLEXIBLE CATEGORIES 328
O. Introduction 328
1. Derivable and permissible rules 329
2. L-decidability 331
3. Deduction theorem and C G 333
4. Preliminary conclusions 335
References 336
Chapter 31. First-Order Logic in Knowledge Graphs 338
1. MOTIVATION 338
2. PROPOSITIONAL KNOWLEDGE GRAPHS 339
3. FROM PROKGS TO PROPOSITIONAL LOGIC 341
4. PREDICATE KNOWLEDGE GRAPHS 342
5. FROM PREKGS TO PREDICATE LOGIC 346
6. CONCLUSIONS 346
REFERENCES 347
Chapter 32. Default Logic as a Tool for Modelling Situations with Exceptions inDiscourse 348
1. INTRODUCTION 349
2 . REPRESENTATION OF A DISCOURSE IN DEFAULT LOGIC 349
3. ANALYSIS OF PARTICULAR MODIFICATIONS WITH RESPECTTO BELIEF-REVISION 353
4. DESCRIPTION OF THE SYSTEM DELORES 356
5. CONCLUSIONS 357
REFERENCES 357
PART IV: APPLICATIONS IN NATURALLANGUAGE PROCESSING 358
Chapter 33. Cartesian Computation and Linguistics in a Current Context 360
1. INTRODUCTION: MATHEMATICAL MODELING AND LANGUAGE 360
2. HOW MATHEMATICS CAN HELP: CARTESIAN COMPUTATIONAND CARTESIAN LEARNING 362
REFERENCES 370
Chapter 34. Context-sensitivity and linguistic structure in analogy-based parallel networks 372
1. THE PROBLEM 372
2. THE ANTAEUS SYSTEM 374
3. AN INSTANCE OF ANTAEUS' LEARNING ROUTINE 376
4. HOW WELL DO ANALOGICAL PATTERNS FARE IN ANALYSIS 378
5. RESULTS OF BOOTSTRAPPING 379
6. CONCLUSION 380
REFERENCES 381
Chapter 35. Declarative Representation and Processing of Systemic Grammars 382
1. INTRODUCTION 382
2. SYSTEMIC GRAMMAR 383
3. THE PROBLEM 384
4. CONJUNCTIVE SYSTEM NETWORKS 384
5. INTRODUCING DISJUNCTION 386
6. IMPLEMENTATION 387
7. CONCLUSION 389
REFERENCES 389
Chapter 36. Dynamic relaxation: measuring the distance from text to grammar 392
DYNAMIC RELAXATION AND CORPUS-BASED PARSING 394
REFERENCES 397
Chapter 37. Modelling Domain and Connectivity Constraintsin Natural Language Processing 400
1 INTRODUCTION 400
2 THE BASIS AND THE ROLE OF THE CONCEPTUAL MODEL 401
3 DOMAIN CONSTRA 402
4 CONNECTIVITY CONSTRAINTS 403
ACKNOWLEDGMENTS 406
REFERENCES 406
CHAPTER 38. SYNTACTIC PRO JECTIVITY IN PROGRAMMINGLANGUAGES (TURBOPASCAL and LOGO) 408
1. INTRODUCTION 408
2. THE LANGUAGE OF ACTIONS WITH A SEMANTIC STRUCTURE 409
3. SUBORDINATION IN THE SENSE OF NEBESKY 412
4. VARIOUS TYPES OF PROJECTIVITY 412
5. THE SYNTACTIC PROJECTIVITY OF TURBOPASCAL 413
6. THE SYNTACTIC PROJECTIVITY OF LOGO 416
REFERENCES 417
Chapter 39. Planning natural language explanations in natural deduction basedsystems 418
1. INTRODUCTION 418
2. NATURAL DEDUCTION SYSTEM 419
3. THE INFORMATIONAL PLANNER 422
4. SELECTION OF EXPLANATION DIRECTRIX 424
5. CONCLUSIONS 426
REFERENCES 426
Chapter 40. 
428 
1. INTRODUCTION 428
2. DESCRIPTION OF QUIP 428
3. CONCLUSION 432
REFERENCES 433
CHAPTER 41. KNOWLEDGE-BASED AUTOMATIC ABSTRACTING:EXPERIMENTS IN THE SUBLANGUAGE OF ELEMENTARYGEOMETRY 434
ABSTRACT 434
1. INTRODUCTION 434
2. KNOWLEDGE: AN INDISPENSABLE PREREQUISITE FOR THESUCCESS OF AN AUTOMATIC ABSTRACTING SYSTEM 435
3. KNOWLEDGE: AN INDISPENSABLE PREREQUISITE FOR THESUCCESS OF AN AUTOMATIC ABSTRACTING SYSTEM 435
4. DOMAIN KNOWLEDGE: WHAT IS IMPORTANT FOR A DOMAIN 437
5. APPLICATION OF THE SUMMARY RULES ON A SAMPLE TEXT 437
6. LINGUISTIC KNOWLEDGE: PARAPHRASING THE SELECTED TEXTINTO A FINAL SUMMARY 438
7. IMPLEMENTATION 439
8. RESTRICTIONS 439
9. POSSIBLE FURTHER INVESTIGATIONS 439
10. CONCLUSION 440
REFERENCES 440
Chapter 42. The Z-Station workbench and the modelling of linguistic knowledge 442
1. GENERAL VIEW OF THE SYSTEM 442
2. MODELLING LINGUISTIC DEPENDENT KNOWLEDGE 443
3. MODELLING INTERLINGUISTIC KNOWLEDGE 446
4. EXAMPLE OF APPLICATION 448
REFERENCES 451
AUTHOR INDEX 452
SUBJECT INDEX 460