Quantifiers in language and logic:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford University Press
2008
|
| Edition: | 1. publ. in paperback |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Originally published: Oxford: Clarendon, 2006 Includes bibliographical references and index |
| Physical Description: | XIX, 528 S. |
| ISBN: | 9780199291267 |
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| 245 | 1 | 0 | |a Quantifiers in language and logic |c Stanley Peters ; Dag Westerståhl |
| 250 | |a 1. publ. in paperback | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford University Press |c 2008 | |
| 300 | |a XIX, 528 S. | ||
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| 500 | |a Originally published: Oxford: Clarendon, 2006 | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Grammar, Comparative and general / Quantifiers | |
| 650 | 4 | |a Grammatik | |
| 650 | 4 | |a Grammar, Comparative and general |x Quantifiers | |
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Record in the Search Index
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| adam_text | Summary Contents
0. Quantification 1
I. THE LOGICAL CONCEPTION OF QUANTIFIERS AND
QUANTIFICATION
1. A Brief Historyof Quantification 21
2. The EmergenceofGeneralizedQuantifiers in Modern Logic 53
II. QUANTIFIERS OF NATURAL LANGUAGE
3. Type (1) QuantifiersofNaturalandLogicalLanguages 79
4. Type (1,1} QuantifiersofNaturalLanguage 119
5. Monotone Quantifiers 163
6. Symmetry and Other Relational Properties of Type (1,1) Quantifiers 208
7. Possessive Quantifiers 242
8. Exceptive Quantifiers 297
9. Which Quantifiers are Logical? 324
10. Some Polyadic Quantifiers of Natural Language 346
III. BEGINNINGS OF A THEORY OF EXPRESSIVENESS,
TRANSLATION, AND FORMALIZATION
11. The Concept of Expressiveness 375
12. Formalization: Expressibility, Definability, Compositionality 414
IV. LOGICAL RESULTS ON EXPRESSIBILITY WITH
LINGUISTIC APPLICATIONS
13. Definability and Undefinability in Logical Languages: Tools for die
Monadic Case 449
14. Applications to Monadic Definability 465
15. EF-tools for Polyadic Quantifiers 483
References 511
Index 521
Detailed Contents
0. Quantification 1
0.1 Some quantifier expressions of natural languages 2
0.2 Varietiesof quantification 10
0.2.1 Syntactic Variation in quantifier expressions 10
0.2.2 Semantic types ofNL quantification 11
0.2.3 Quantirelations 13
0.3 Explicit and implicit quantification 15
0.4 Monadic and polyadic quantifiers 16
I THE LOGICAL CONCEPTION OF QUANTIFIERS AND
QUANTIFICATION
1. A Brief Historyof Quantification 21
*1.1 Early histoty of quantifiers 22
1.1.1 Aristotelian beginnings 22
1.1.2 TheMiddleAges 30
1.2 Quantifiers in early predicate logic 34
1.2.1 Peirce 35
1.2.2 Peano 36
1.2.3 Russell 36
1.2.4 Frege 38
1.3 Truth and modeis 40
1.3.1 Absolute and relative truth 40
1.3.2 Uninterpreted symbols 41
1.3.3 Universes 42
1.3.4 Contextsets 44
*1.3.5 Quantifying over everything? 47
*1.4 PostScript: Why quantifiers cannot denote individuals
or sets of individuals 49
2. The Emergence of Generalized Quantifiers in Modern Logic 53
*2.1 First-order logic versus first-order languages 53
2.2 First-order logic (FO) 56
2.3 Mostowski quantifiers 59
2.4 Lindström quantifiers 62
xiv Detailed Contents
2.5 Branching quantifiers 66
2.5.1 First-order sentences making second-order daims 68
2.5.2 Branching generalized quantifiers 70
2.6 Digression: why logicians like FO 72
2.7 Summary 73
II QUANTIFIERS OF NATURAL LANGUAGE
3. Type (1) Quantifiers of Natural and Logical Languages 79
3.1 Preliminary concepts and distinctions 80
3.1.1 Global and local quantifiers 80
3.1.2 Quantifier expressions versus predicate expressions 83
3.1.3 Relational and functional views of quantifiers 84
3.2 Phrases denoting type (1) quantifiers °
3.2.1 Examples of nounphrase denotations 86
*3.2.2 Quantifiers living on sets 89
3.2.3 Boolean operations on quantifiers 91
3.2.4 Montagovian individuals 93
3.3 Isomorphism closure • -
3.3.1 Isom for type (1) quantifiers 95
3.3.2 Isom for arbitrary quantifiers 98
3.4 Extension 10°
3.4.1 Ext as a property of quantifiers 101
3.4.2 Ext and database languages 107
*3.5 How natural language quantifier expressions always denote
global quantifiers ^
3.5.1 Sense and local denotation 112
3.5.2 Using global quantifiers 114
3.5.3 Examples 116
4. Type (1,1} Quantifiers of Natural Language ^
4.1 Examples ofdeterminers ^
*4.2 On existential import and related matters *
4.2.1 Existential import 124
4.2.2 Syntactic and semantic number 128
4.3 Boolean operations ^
4.4 Relativization ^
4.4.1 Examples 135
4.4.2 Empty universes 137
4.5 Conservativity, extension, and relativization
4.5.1 Conservativity 138
4.5.2 A quantirelation universal 138
*4.5.3 An extension universal 140
4.5.4 The relativization characterization 141
*4.5.5 Restricted quantifiers once again 143
I
Detailed Contents xv
4.6 Definiteness 149
4.7 Type (1,1,1) quantifiers and. beyond 153
4.8 Isom and die number oiangle 157
5. Monotone Quantifiers 163
5.1 Standard monotonicity 164
5.2 Monotonicity in type (1,1) 168
5.3 Monotonicity universals 172
5.4 Monotonicity under Isom 174
5.4.1 A format for monotone quantifiers ovcr finite universes 174
5.4.2 Monotonicity and the number triangle 176
*5.5 Six basic forms of monotonicity 178
5.6 Smooth quantifiers 185
*5.7 Linguistic application 1: a peculiar inference scheme 191
*5.8 Linguistic application 2: LAA quantifiers 192
*5.9 Linguistic application 3: polarity-sensitive items
in natural languages 196
5.9.1 What are NPIs and PPIs sensitive to? 197
5.9.2 What is negative about negation? 199
5.9.3 A hypothesis about licensing of NPIs and PPIs 201
5.9.4 Testing the hypothesis 204
6. Symmetry and Other Relational Properties of Type (1,1) Quantifiers 208
6.1 Symmetry 208
6.2 On the symmetry oi many and fiw 213
*6.3 Existential-there sentences 214
6.3.1 Natural language talk about existence 214
6.3.2 Restrictions on the pivot noun phrase
of existential-there sentences 217
6.3.3 What do existential-there sentences mean? 220
6.3.4 Four approaches to distinguishing between existentially
acceptable determinets and existentially unacceptable ones 225
6.3.5 Some additional data and conclusions 235
6.4 Other relational properties of Consekv
and Ext type (1,1) quantifiers 237
*7. Possessive Quantifiers 242
7.1 Possessive determiners and NPs 244
7.2 Number and uniqueness 246
7.3 Universal readings and others 247
7.4 Scope ambiguities? 249
7-5 Narrowing 250
7.6 The possessor relation 251
7-7 The meaning of possessive determiners 254
xyj Detailed Contents
7.8 Alternative accounts 259
7.8.1 Poss without narrowing 259
7.8.2 A definiteness account 261
7.8.3 A problem with thesg and thepi 262
7.8.4 Narrowing versus accommodation 263
7.8.5 Summingup 264
73 Semantic rules for possessives 266
7.10 Iterated possessives 272
7.11 Definites and possessives 276
7.11.1 Which possessives are definite? 276
7.11.2 What makes an expression definite? 277
7.11.3 A semantic rule for the definite case 280
7.12 Closure properties of Poss 282
7.12.1 Negations 283
7.12.2 Conjunctions and disjunctions 284
7.12.3 Some odier determiners involving possessives 286
7.12.4 Restrictions on the (poss) rule 287
7.13 Possessives and monotonicity 288
IOC
7.14 Some remaining issues l- -
*8. Exceptive Quantifiers 297
8.1 Connected and free exception phrases ^
8.2 The Generality Claim 300
8.3 The Inclusion Condition 300
8.4 Exception conservativity •*
8.5 The Negative Condition 302
8.6 Entailed or implicated? 304
8.7 Other quantifiers in exception sentences 304
8.8 The classicalideaof universal claims with exceptions 303
8.9 The account in von Fintel 1993 306
8.10 The account in Moltmann 1995 31°
8.11 Counter-evidence to the Quantifier Constraint 312
8.12 A modest proposal *
8.13 Quantified exception phrases 31°
8.14 Further ässues 322
9. Which Quantifiers are Logical? 324
9.1 Logicality and Isom 324
9.1.1 Isom in arbitrary types 325
9.1.2 Isom is necessarv for logicality 327
9.1.3 Strengthening Isom 328
*9.2 Two claims about Isom and natural language quantification 330
9.2.1 Proper names 331
9.2.2 Restricted noun phrases 332
9.2.3 Possessives 332
I
Detaikd Contents xvii
9.2.4 Exceptive quantifiers 333
*9.3 Constancy 334
9.3.1 Inference constancy 334
9.3.2 Bolzano s method 335
9.3.3 Bolzano reversed 337
9.3.4 What to interpret in modeis 341
9.4 Logical constants 343
9.4.1 Logic versus mathematics 343
9.4.2 Isom + Ext 344
10. Some Polyadic Quantifiers of Natural Language 346
10.1 Iteration 346
10.2 Resumption 352
10.2.1 Quantificational adverbs and donkey anaphora 354
10.2.2 Resumption, orientation, and tuple-isomorphisms 359
10.3 Branching 363
10.4 Reciprocals 364
10.4.1 What do reciprocals mean? 365
10.4.2 Type (1,2) reciprocal quantifiers 367
10.4.3 Properties of reciprocal quantifiers 368
*10.4.4 Collective predicates formed with reciprocals, and quantification
of such predicates 369
III BEGINNINGSOFATHEORY
OF EXPRESSIVENESS, TRANSLATION, AND
FORMALIZATION
* 11. The Concept of Expressiveness 375
11.1 Preliminaries 376
11.1.1 Three levels of expressions 376
11.1.2 Expressibility of quantifier expressions
versus predicate expressions 380
11.2 A framework for translation 382
11.2.1 Expressiveness is relative to a notion
ofsayingthesame thing 382
11.2.2 Sameness of meaning, without meanings 383
11.2.3 Sameness is a partial equivalence felation (PER) 385
11.2.4 Translation and formalization 390
11.3 Varieries of sameness 397
11.3.1 Sameness ofdenotation 397
11.3.2 Logical equivalence 400
11.3.3 Analytical/necessary equivalence 403
11.3.4 Varieties of cognitive equivalence 405
11.3-5 Possible Iinguistic equivalences 407
11.3.6 The ultimate refinement: identitf 410
xyüi Detailed Contents
11.3.7 Where do relations of synonymy come fern! 410
11.3.8 Alandscape of possible synonymies 412
*12. Formalization: Expressibility, Definability, Compositionality 414
12.1 Logical equivalence revisited 414
12.1.1 Lexical mappings 415
12.1.2 Logical equivalence relative to a lexical mapping 418
12.2 Compositionality 421
12.2.1 Compositional languages 422
12.2.2 Compositional translation 424
12.3 Requirements on definitions 428
12.4 Extending lexical mappings to compositional translations 432
12.4.1 Definable gratnmar rules 433
12.4.2 An extension theotem 435
12.5 Why formal definability results matter for natural languages 437
12.5.1 The role of lexical mappings 438
12.5.2 Uniform expressivity 439
12.5.3 Meaning postulates and expressivity 441
12.5.4 The role of formalization 442
12.5.5 Summingup 444
IV LOGICAL RESULTS ON EXPRESSIBILITY WITH
LINGUISTIC APPLICATIONS
13. Definability and Undefinability in Logical Languages: Tools for the
Monadic Case 449
13.1 Logics with quantifiers 449
13.2 Definabiiity 451
13.2.1 Examples of definability 452
13.2.2 The role oflsoM 455
13.3 Undefinability 455
13.4 EF-tools for the monadic case 457
13.4.1 The structure of monadic modeis 457
13.4.2 A criterion for Z7-equivalence over monadic modeis 458
13.4.3 Proofthat the criterion iscorrect 460
14. Applications to Monadic Definability 465
14.1 Themethod 465
14.2 .FO-undefinability 466
14.3 Undefinability in other logics 469
14.4 Monotonicity and definability 476
14.5 Exerdses 481
i
Detailed Contents xix
15. EF-tools for Polyadic Quantifiers 483
15.1 EF-games 483
15.2 HellasbijectiveEF-game 491
15.3 AppHcation to branching quantification 494
15.3.1 An instructive example 495
15.3.2 The general result 495
15.3.3 Linguistic conclusions 498
15.4 Application to Ramsey quantifiers and reciprocals 498
15.4.1 A characterization theorem 498
15.4.2 Linguistic conclusions 499
15.5 Application to resumption and adverbial quantification 500
15.5.1 Definability in terms of resumptive quantifiers 500
15.5-2 Linguistic consequences, 1 502
15.5.3 Definability of resumption 503
15.5.4 Linguistic consequences, 2 508
References 511
Index 521
Index of Symbols 527
|
| adam_txt |
Summary Contents
0. Quantification 1
I. THE LOGICAL CONCEPTION OF QUANTIFIERS AND
QUANTIFICATION
1. A Brief Historyof Quantification 21
2. The EmergenceofGeneralizedQuantifiers in Modern Logic 53
II. QUANTIFIERS OF NATURAL LANGUAGE
3. Type (1) QuantifiersofNaturalandLogicalLanguages 79
4. Type (1,1} QuantifiersofNaturalLanguage 119
5. Monotone Quantifiers 163
6. Symmetry and Other Relational Properties of Type (1,1) Quantifiers 208
7. Possessive Quantifiers 242
8. Exceptive Quantifiers 297
9. Which Quantifiers are Logical? 324
10. Some Polyadic Quantifiers of Natural Language 346
III. BEGINNINGS OF A THEORY OF EXPRESSIVENESS,
TRANSLATION, AND FORMALIZATION
11. The Concept of Expressiveness 375
12. Formalization: Expressibility, Definability, Compositionality 414
IV. LOGICAL RESULTS ON EXPRESSIBILITY WITH
LINGUISTIC APPLICATIONS
13. Definability and Undefinability in Logical Languages: Tools for die
Monadic Case 449
14. Applications to Monadic Definability 465
15. EF-tools for Polyadic Quantifiers 483
References 511
Index 521
Detailed Contents
0. Quantification 1
0.1 Some quantifier expressions of natural languages 2
0.2 Varietiesof quantification 10
0.2.1 Syntactic Variation in quantifier expressions 10
0.2.2 Semantic types ofNL quantification 11
0.2.3 Quantirelations 13
0.3 Explicit and implicit quantification 15
0.4 Monadic and polyadic quantifiers 16
I THE LOGICAL CONCEPTION OF QUANTIFIERS AND
QUANTIFICATION
1. A Brief Historyof Quantification 21
*1.1 Early histoty of quantifiers 22
1.1.1 Aristotelian beginnings 22
1.1.2 TheMiddleAges 30
1.2 Quantifiers in early predicate logic 34
1.2.1 Peirce 35
1.2.2 Peano 36
1.2.3 Russell 36
1.2.4 Frege 38
1.3 Truth and modeis 40
1.3.1 Absolute and relative truth 40
1.3.2 Uninterpreted symbols 41
1.3.3 Universes 42
1.3.4 Contextsets 44
*1.3.5 Quantifying over everything? 47
*1.4 PostScript: Why quantifiers cannot denote individuals
or sets of individuals 49
2. The Emergence of Generalized Quantifiers in Modern Logic 53
*2.1 First-order logic versus first-order languages 53
2.2 First-order logic (FO) 56
2.3 Mostowski quantifiers 59
2.4 Lindström quantifiers 62
xiv Detailed Contents
2.5 Branching quantifiers 66
2.5.1 First-order sentences making second-order daims 68
2.5.2 Branching generalized quantifiers 70
2.6 Digression: why logicians like FO 72
2.7 Summary 73
II QUANTIFIERS OF NATURAL LANGUAGE
3. Type (1) Quantifiers of Natural and Logical Languages 79
3.1 Preliminary concepts and distinctions 80
3.1.1 Global and local quantifiers 80
3.1.2 Quantifier expressions versus predicate expressions 83
3.1.3 Relational and functional views of quantifiers 84
3.2 Phrases denoting type (1) quantifiers °"
3.2.1 Examples of nounphrase denotations 86
*3.2.2 Quantifiers living on sets 89
3.2.3 Boolean operations on quantifiers 91
3.2.4 Montagovian individuals 93
3.3 Isomorphism closure •'-'
3.3.1 Isom for type (1) quantifiers 95
3.3.2 Isom for arbitrary quantifiers 98
3.4 Extension 10°
3.4.1 Ext as a property of quantifiers 101
3.4.2 Ext and database languages 107
*3.5 How natural language quantifier expressions always denote
global quantifiers ^
3.5.1 Sense and local denotation 112
3.5.2 Using global quantifiers 114
3.5.3 Examples 116
4. Type (1,1} Quantifiers of Natural Language ^
4.1 Examples ofdeterminers ^
*4.2 On existential import and related matters *
4.2.1 Existential import 124
4.2.2 Syntactic and semantic number 128
4.3 Boolean operations ^
4.4 Relativization ^
4.4.1 Examples 135
4.4.2 Empty universes 137
4.5 Conservativity, extension, and relativization
4.5.1 Conservativity 138
4.5.2 A quantirelation universal 138
*4.5.3 An extension universal 140
4.5.4 The relativization characterization 141
*4.5.5 Restricted quantifiers once again 143 '
I
Detailed Contents xv
4.6 Definiteness 149
4.7 Type (1,1,1) quantifiers and. beyond 153
4.8 Isom and die number oiangle 157
5. Monotone Quantifiers 163
5.1 Standard monotonicity 164
5.2 Monotonicity in type (1,1) 168
5.3 Monotonicity universals 172
5.4 Monotonicity under Isom 174
5.4.1 A format for monotone quantifiers ovcr finite universes 174
5.4.2 Monotonicity and the number triangle 176
*5.5 Six basic forms of monotonicity 178
5.6 Smooth quantifiers 185
*5.7 Linguistic application 1: a peculiar inference scheme 191
*5.8 Linguistic application 2: LAA quantifiers 192
*5.9 Linguistic application 3: polarity-sensitive items
in natural languages 196
5.9.1 "What are NPIs and PPIs sensitive to? 197
5.9.2 What is negative about negation? 199
5.9.3 A hypothesis about licensing of NPIs and PPIs 201
5.9.4 Testing the hypothesis 204
6. Symmetry and Other Relational Properties of Type (1,1) Quantifiers 208
6.1 Symmetry 208
6.2 On the symmetry oi many and fiw 213
*6.3 Existential-there sentences 214
6.3.1 Natural language talk about existence 214
6.3.2 Restrictions on the pivot noun phrase
of existential-there sentences 217
6.3.3 What do existential-there sentences mean? 220
6.3.4 Four approaches to distinguishing between existentially
acceptable determinets and existentially unacceptable ones 225
6.3.5 Some additional data and conclusions 235
6.4 Other relational properties of Consekv
and Ext type (1,1) quantifiers 237
*7. Possessive Quantifiers 242
7.1 Possessive determiners and NPs 244
7.2 Number and uniqueness 246
7.3 Universal readings and others 247
7.4 Scope ambiguities? 249
7-5 Narrowing 250
7.6 The possessor relation 251
7-7 The meaning of possessive determiners 254
xyj Detailed Contents
7.8 Alternative accounts 259
7.8.1 Poss without narrowing 259
7.8.2 A definiteness account 261
7.8.3 A problem with thesg and thepi 262
7.8.4 Narrowing versus accommodation 263
7.8.5 Summingup 264
73 Semantic rules for possessives 266
7.10 Iterated possessives 272
7.11 Definites and possessives 276
7.11.1 Which possessives are definite? 276
7.11.2 What makes an expression definite? 277
7.11.3 A semantic rule for the definite case 280
7.12 Closure properties of Poss 282
7.12.1 Negations 283
7.12.2 Conjunctions and disjunctions 284
7.12.3 Some odier determiners involving possessives 286
7.12.4 Restrictions on the (poss) rule 287
7.13 Possessives and monotonicity 288
IOC
7.14 Some remaining issues l-'-
*8. Exceptive Quantifiers 297
8.1 Connected and free exception phrases ^"
8.2 The Generality Claim 300
8.3 The Inclusion Condition 300
8.4 Exception conservativity •*
8.5 The Negative Condition 302
8.6 Entailed or implicated? 304
8.7 Other quantifiers in exception sentences 304
8.8 The classicalideaof universal claims with exceptions 303
8.9 The account in von Fintel 1993 306
8.10 The account in Moltmann 1995 31°
8.11 Counter-evidence to the Quantifier Constraint 312
8.12 A modest proposal *
8.13 Quantified exception phrases 31°
8.14 Further ässues 322
9. Which Quantifiers are Logical? 324
9.1 Logicality and Isom 324
9.1.1 Isom in arbitrary types 325
9.1.2 Isom is necessarv for logicality 327
9.1.3 Strengthening Isom 328
*9.2 Two claims about Isom and natural language quantification 330
9.2.1 Proper names 331
9.2.2 Restricted noun phrases 332
9.2.3 Possessives 332
I
Detaikd Contents xvii
9.2.4 Exceptive quantifiers 333
*9.3 Constancy 334
9.3.1 Inference constancy 334
9.3.2 Bolzano's method 335
9.3.3 Bolzano reversed 337
9.3.4 What to interpret in modeis 341
9.4 Logical constants 343
9.4.1 Logic versus mathematics 343
9.4.2 Isom + Ext 344
10. Some Polyadic Quantifiers of Natural Language 346
10.1 Iteration 346
10.2 Resumption 352
10.2.1 Quantificational adverbs and 'donkey' anaphora 354
10.2.2 Resumption, orientation, and tuple-isomorphisms 359
10.3 Branching 363
10.4 Reciprocals 364
10.4.1 What do reciprocals mean? 365
10.4.2 Type (1,2) reciprocal quantifiers 367
10.4.3 Properties of reciprocal quantifiers 368
*10.4.4 Collective predicates formed with reciprocals, and quantification
of such predicates 369
III BEGINNINGSOFATHEORY
OF EXPRESSIVENESS, TRANSLATION, AND
FORMALIZATION
* 11. The Concept of Expressiveness 375
11.1 Preliminaries 376
11.1.1 Three levels of expressions 376
11.1.2 Expressibility of quantifier expressions
versus predicate expressions 380
11.2 A framework for translation 382
11.2.1 Expressiveness is relative to a notion
ofsayingthesame thing 382
11.2.2 Sameness of meaning, without meanings 383
11.2.3 Sameness is a partial equivalence felation (PER) 385
11.2.4 Translation and formalization 390
11.3 Varieries of sameness 397
11.3.1 Sameness ofdenotation 397
11.3.2 Logical equivalence 400
11.3.3 Analytical/necessary equivalence 403
11.3.4 Varieties of cognitive equivalence 405
11.3-5 Possible Iinguistic equivalences 407
11.3.6 The ultimate refinement: identitf 410
xyüi Detailed Contents
11.3.7 Where do relations of synonymy come fern! 410
11.3.8 Alandscape of possible synonymies 412
*12. Formalization: Expressibility, Definability, Compositionality 414
12.1 Logical equivalence revisited 414
12.1.1 Lexical mappings 415
12.1.2 Logical equivalence relative to a lexical mapping 418
12.2 Compositionality 421
12.2.1 Compositional languages 422
12.2.2 Compositional translation 424
12.3 Requirements on definitions 428
12.4 Extending lexical mappings to compositional translations 432
12.4.1 Definable gratnmar rules 433
12.4.2 An extension theotem 435
12.5 Why formal definability results matter for natural languages 437
12.5.1 The role of lexical mappings 438
12.5.2 Uniform expressivity 439
12.5.3 Meaning postulates and expressivity 441
12.5.4 The role of formalization 442
12.5.5 Summingup 444
IV LOGICAL RESULTS ON EXPRESSIBILITY WITH
LINGUISTIC APPLICATIONS
13. Definability and Undefinability in Logical Languages: Tools for the
Monadic Case 449
13.1 Logics with quantifiers 449
13.2 Definabiiity 451
13.2.1 Examples of definability 452
13.2.2 The role oflsoM 455
13.3 Undefinability 455
13.4 EF-tools for the monadic case 457
13.4.1 The structure of monadic modeis 457
13.4.2 A criterion for Z7-equivalence over monadic modeis 458
13.4.3 Proofthat the criterion iscorrect 460
14. Applications to Monadic Definability 465
14.1 Themethod 465
14.2 .FO-undefinability 466
14.3 Undefinability in other logics 469
14.4 Monotonicity and definability 476
14.5 Exerdses 481
i
Detailed Contents xix
15. EF-tools for Polyadic Quantifiers 483
15.1 EF-games 483
15.2 HellasbijectiveEF-game 491
15.3 AppHcation to branching quantification 494
15.3.1 An instructive example 495
15.3.2 The general result 495
15.3.3 Linguistic conclusions 498
15.4 Application to Ramsey quantifiers and reciprocals 498
15.4.1 A characterization theorem 498
15.4.2 Linguistic conclusions 499
15.5 Application to resumption and adverbial quantification 500
15.5.1 Definability in terms of resumptive quantifiers 500
15.5-2 Linguistic consequences, 1 502
15.5.3 Definability of resumption 503
15.5.4 Linguistic consequences, 2 508
References 511
Index 521
Index of Symbols 527 |
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| discipline | Sprachwissenschaft Literaturwissenschaft |
| discipline_str_mv | Sprachwissenschaft Literaturwissenschaft |
| edition | 1. publ. in paperback |
| format | Book |
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| id | DE-604.BV023273461 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:36:54Z |
| indexdate | 2024-07-09T21:14:41Z |
| institution | BVB |
| isbn | 9780199291267 |
| language | English |
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| spelling | Peters, Stanley 1941- Verfasser (DE-588)135786363 aut Quantifiers in language and logic Stanley Peters ; Dag Westerståhl 1. publ. in paperback Oxford [u.a.] Oxford University Press 2008 XIX, 528 S. txt rdacontent n rdamedia nc rdacarrier Originally published: Oxford: Clarendon, 2006 Includes bibliographical references and index Grammar, Comparative and general / Quantifiers Grammatik Grammar, Comparative and general Quantifiers Quantor (DE-588)4128275-9 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Quantifizierung Linguistik (DE-588)4076453-9 gnd rswk-swf Quantifizierung Linguistik (DE-588)4076453-9 s DE-604 Quantor (DE-588)4128275-9 s Prädikatenlogik (DE-588)4046974-8 s Westerståhl, Dag 1946- Verfasser (DE-588)131805355 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016458418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peters, Stanley 1941- Westerståhl, Dag 1946- Quantifiers in language and logic Grammar, Comparative and general / Quantifiers Grammatik Grammar, Comparative and general Quantifiers Quantor (DE-588)4128275-9 gnd Prädikatenlogik (DE-588)4046974-8 gnd Quantifizierung Linguistik (DE-588)4076453-9 gnd |
| subject_GND | (DE-588)4128275-9 (DE-588)4046974-8 (DE-588)4076453-9 |
| title | Quantifiers in language and logic |
| title_auth | Quantifiers in language and logic |
| title_exact_search | Quantifiers in language and logic |
| title_exact_search_txtP | Quantifiers in language and logic |
| title_full | Quantifiers in language and logic Stanley Peters ; Dag Westerståhl |
| title_fullStr | Quantifiers in language and logic Stanley Peters ; Dag Westerståhl |
| title_full_unstemmed | Quantifiers in language and logic Stanley Peters ; Dag Westerståhl |
| title_short | Quantifiers in language and logic |
| title_sort | quantifiers in language and logic |
| topic | Grammar, Comparative and general / Quantifiers Grammatik Grammar, Comparative and general Quantifiers Quantor (DE-588)4128275-9 gnd Prädikatenlogik (DE-588)4046974-8 gnd Quantifizierung Linguistik (DE-588)4076453-9 gnd |
| topic_facet | Grammar, Comparative and general / Quantifiers Grammatik Grammar, Comparative and general Quantifiers Quantor Prädikatenlogik Quantifizierung Linguistik |
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