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E-raamat: Quantifiers and Cognition: Logical and Computational Perspectives

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Quantifiers and Cognition: Logical and Computational PerspectivesSuurem pilt
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This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition.  Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of quantifier expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in lin

guistics, philosophy, cognitive science, logic, AI, and computer science. 

Introduction.- Acknowledgments.- Part I: Procedural Semantics.- 1. Algorithmic Theory of Meaning.- 2. Complexity in Linguistics.- Part II: Simple Quantifiers.- 3. Basic Generalized Quantifier Theory.- 4. Computing Simple Quantifiers.- 5. Cognitive Processing of Quantifiers.- Part III: Complex Quantifiers.- 6. Standard Polyadic Lifts.- 7. Complexity of Polyadic Quantifiers.- 8. Complexity of Quantified Reciprocals.- 9. Branching Quantifiers.- Part IV: Collective Quantifiers.- 10. Complexity of Collective Quantification.- Part V: Perspectives and Conclusions.- Conclusions.- A. Mathematical Machinery.- Bibliography.- Subject Index

Arvustused

Jakub Szymanik has produced an important new book, Quantifiers and Cognition: Logical and Computational Perspectives which returns logic to center stage in an important area of human cognitive studies, where the psychology and neuroscience of language, number and reasoning intersect and interact. the book is a valuable source of new results for the theoretician, and a gold mine for the experimenter. (Giosue Baggio and Heming Strømholt Bremnes, Studia Logica, Vol. 105, 2017)

Part I Procedural Semantics
1 Algorithmic Theory of Meaning
3(6)
References
7(2)
2 Complexity in Linguistics
9(14)
2.1 Computational Complexity
10(1)
2.2 Syntax
11(2)
2.3 Descriptive Syntax
13(1)
2.4 Semantics
13(4)
2.5 Finite Universes
17(6)
References
18(5)
Part II Simple Quantifiers
3 Basic Generalized Quantifier Theory
23(18)
3.1 Two Equivalent Concepts of Generalized Quantifiers
25(2)
3.2 Logic Enriched by Generalized Quantifiers
27(1)
3.3 Definability of Generalized Quantifiers
27(3)
3.4 Semantic Universals
30(6)
3.4.1 Boolean Combinations of Quantifiers
30(1)
3.4.2 Relativization of Quantifiers
31(1)
3.4.3 Domain Independence
31(1)
3.4.4 Conservativity
32(1)
3.4.5 CE-Quantifiers
33(3)
3.5 Monotonicity
36(5)
References
39(2)
4 Computing Simple Quantifiers
41(10)
4.1 Representation of Finite Models
42(2)
4.2 Quantifier Automata
44(2)
4.3 Characterization Results
46(5)
References
49(2)
5 Cognitive Processing of Quantifiers
51(36)
5.1 Processing Time
54(3)
5.1.1 Experiment 1
54(2)
5.1.2 Experiment 2
56(1)
5.2 Accuracy
57(4)
5.2.1 Probabilistic Semantic Automata
57(2)
5.2.2 Modeling the Data
59(2)
5.3 Working Memory
61(6)
5.3.1 Neurocognitive Evidence
61(1)
5.3.2 Concurrent Tasks
62(1)
5.3.3 Schizophrenic Patients
63(2)
5.3.4 Intelligence
65(1)
5.3.5 Executive Resources
65(2)
5.4 Corpora Distributions
67(2)
5.4.1 Power Laws
68(1)
5.5 Monotonicity
69(7)
5.5.1 Comparison with Literature
74(2)
5.6 Approximate Number System
76(2)
5.7 Discussion
78(9)
References
80(7)
Part III Complex Quantifiers
6 Standard Polyadic Lifts
87(14)
6.1 Iteration
88(2)
6.2 Cumulation
90(1)
6.3 Resumption
90(1)
6.4 Semantic Automata for Polyadic Quantifiers
91(4)
6.4.1 Experimental Direction
94(1)
6.5 The Frege Boundary
95(5)
6.5.1 Classic Characterization Results
96(3)
6.5.2 The Frege Boundary and the Chomsky Hierarchy?
99(1)
6.6 Summary
100(1)
References
100(1)
7 Complexity of Polyadic Quantifiers
101(22)
7.1 Computational Complexity of Quantifiers
102(4)
7.2 PTIME Generalized Quantifiers Are Closed Under It, Cum, and Res
106(2)
7.3 Branching Quantifiers
108(3)
7.3.1 Henkin's Quantifiers
109(1)
7.3.2 Proportional Branching Quantifiers
109(2)
7.4 Ramsey Quantifiers
111(8)
7.4.1 The Branching Reading of Hintikka's Sentence
111(1)
7.4.2 Clique Quantifiers
112(1)
7.4.3 Proportional Ramsey Quantifiers
113(2)
7.4.4 Tractable Ramsey Quantifiers
115(2)
7.4.5 Intermediate Ramsey Quantifiers
117(1)
7.4.6 Dichotomy Result
118(1)
7.5 Summary
119(4)
References
120(3)
8 Complexity of Quantified Reciprocals
123(20)
8.1 Reciprocal Expressions
124(4)
8.1.1 Strong Meaning Hypothesis
127(1)
8.2 Reciprocals as Polyadic Quantifiers
128(2)
8.2.1 Strong Reciprocal Lift
128(1)
8.2.2 Intermediate Reciprocal Lift
129(1)
8.2.3 Weak Reciprocal Lift
129(1)
8.2.4 The Reciprocal Lifts in Action
129(1)
8.3 Complexity of Strong Reciprocity
130(4)
8.3.1 Counting Quantifiers in the Antecedent
131(1)
8.3.2 Proportional Quantifiers in the Antecedent
132(1)
8.3.3 Tractable Strong Reciprocity
133(1)
8.4 Intermediate and Weak Lifts
134(2)
8.5 A Complexity Perspective on the SMH
136(1)
8.6 Empirical Evidence
137(3)
8.6.1 Cognitive Difficulty
137(2)
8.6.2 Distribution in English
139(1)
8.7 Summary
140(3)
References
141(2)
9 Branching Quantifiers
143(22)
9.1 Hintikka's Thesis
144(2)
9.2 Other Hintikka-Like Sentences
146(1)
9.3 Theoretical Discussion
147(6)
9.3.1 A Remark on Possible Readings
147(1)
9.3.2 Hintikka-Like Sentences Are Symmetric
148(1)
9.3.3 Inferential Arguments
149(1)
9.3.4 Negation Normality
150(2)
9.3.5 Complexity Arguments
152(1)
9.3.6 Theoretical Conclusions
152(1)
9.4 Empirical Evidence
153(6)
9.4.1 Experimental Hypotheses
153(1)
9.4.2 Experiments
154(5)
9.5 Summary
159(6)
References
160(5)
Part IV Collective Quantifiers
10 Complexity of Collective Quantification
165(22)
10.1 Collective Quantifiers
166(3)
10.1.1 Collective Readings in Natural Language
166(2)
10.1.2 Modeling Collectivity
168(1)
10.2 Lifting First-Order Determiners
169(5)
10.2.1 The Existential Modifier
169(2)
10.2.2 The Neutral Modifier
171(1)
10.2.3 The Determiner Fitting Operator
171(1)
10.2.4 A Note on Collective Invariance Properties
172(2)
10.3 Second-Order Generalized Quantifiers
174(1)
10.4 Defining Collective Determiners by SOGQs
175(2)
10.5 Definability Theory for SOGQs
177(3)
10.5.1 Basic Facts
177(2)
10.5.2 Characterization Result
179(1)
10.6 Collective Majority
180(3)
10.6.1 An Undefinability Result for the SOGQ `MOST'
180(1)
10.6.2 Consequences of Undefinability
181(2)
10.7 Summary
183(4)
References
184(3)
Part V Perspectives and Conclusions
11 Conclusions
187(4)
References
189(2)
Appendix A Mathematical Machinery 191(18)
Index 209
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