Cover
Contents
Preface
1. The Roots of Infinity
1.1 The Roots of Infinity in Natural Language
1.2 Boolean Compounding
1.3 References
2.1 More about Sets
2.2 Sequences
2.3 Functions and Sequences
2.4 Arbitrary Unions and Intersections
2.5 Definitions by Closure (Recursion)
2.6 Bijections and the Sizes of Cross Products
2.7 A Linguistic Function
2.8 A Closing Reflection on Functions
2.10 Addendum 1: Russell's Paradox
2.11 Addendum 2: An Equivalent, Useful, Definition of Closure
2.12 Addendum 3: Some Initial Hints on Setting up Proofs
3. Boolean Phonology
3.1 Abstract Segmental Phonology
3.2 Enriching Feature Sets
3.3 Some Phonological Generalizations
3.4 The Mathematical Structure of Feature Sets
3.5 Significant Sound Segments
4. Syntax I: Trees and Order Relations
4.1 Trees
4.2 C-Command
4.3 Sameness of Structure: Isomorphism
4.4 Labeled Trees
4.5 Ordered Trees
4.6 Concluding Formal Exercises on Relations and Ordered Trees
5. Syntax II: Design for a Language
5.1 Beginning Grammar
5.2 Eng—Towards a Grammar of English
5.3 Word Order Variation in Other Languages
5.4 Three New Types of DPs
6.1 Introduction
6.2 CFGs: A Formal Definition
6.3 How Well Do CFGs Model Natural Languages?
7. Finite State Automata
7.1 Finite-State Automata
7.2 Regular Expressions and Languages
7.3 Simple Grammars
7.4 Closing the Circle
7.5 an bn is not a Regular Language
7.6 An Argument Why English is Not Regular
7.7 Two Final Observations on Finite State Automata
8.1 Compositionality and Natural Language Semantics
8.2 Sentential Logic
8.3 Interpreting a Fragment of English
9. Semantics II: Coordination, Negation and Lattices
9.1 Coordination: Syntax
9.2 Coordination: Semantics
9.3 Negation and Additional Properties of Natural Language Lattices
9.4 Properties versus Sets: Lattice Isomorphisms
9.5 Theorems on Boolean Lattices
9.6 Some (Possibly) Unexpected Boolean Lattices
9.7 A Concluding Note on Point of View
9.9 Appendix: Tarski-Knaster and Schröder-Bernstein
10.1 Translation Semantics
10.2 Some General Linguistic Properties of First Order Logic (FOL)
10.3 Extending the Class of VBO's: The Lambda Operator
11.1 Negative Polarity Items
11.2 Monotonicity
11.3 Semantic Generalizations
11.4 Historical Background
12. Semantics V: Classifying Quantifiers
12.1 Quantifier Types
12.2 Generalizations Concerning Det Denotations
12.3 k-Place Dets
12.4 Crossing the Frege Boundary
12.5 A Classic Syntactic Problem
12.6 Adverbial Quantification
12.7 Concluding Remarks
12.9 Appendix: Some Types of English Determiners
13. Linguistic Invariants
13.1 A Model Grammar and Some Basic Theorems
13.2 A Semantic Definition of Anaphor
13.3 A Model of Korean
13.4 Toba Batak
13.5 Some Mathematical Properties of Grammars and their Invariants
13.6 Invariants of Type 0
13.7 Invariants of Type (1)
13.8 Invariants of Type (2) and Higher
13.9 Structure Preserving Operations on Grammars
The Greek Alphabet
Bibliography
Subject Index
Back Cover