Mathematical Structures in Languages (Lecture Notes)

Synopsis

Machine Generated Contents Note: 1.1. 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. Linguistic Function -- 2.8. Closing Reflection On Functions -- 2.9. Suggestions For Further Study -- 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 -- 3.1. Abstract Segmental Phonology -- 3.2. Enriching Feature Sets -- 3.3. Some Phonological Generalizations -- 3.4. Mathematical Structure Of Feature Sets -- 3.5. Significant Sound Segments -- 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 -- 5.1. 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? -- 7.1. Finite-state Automata -- 7.2. Regular Expressions And Languages -- 7.3. Simple Grammars -- 7.4. Closing The Circle -- 7.5. Anbn Is Not A Regular Language -- 7.6. 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 -- 9.1. 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. Concluding Note On Point Of View -- 9.8. Further Reading -- 9.9. Appendix: Tarski-knaster And Schroder-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 -- 12.1. Quantifier Types -- 12.2. Generalizations Concerning Det Denotations -- 12.3. K-place Dets -- 12.4. Crossing The Frege Boundary -- 12.5. Classic Syntactic Problem -- 12.6. Adverbial Quantification -- 12.7. Concluding Remarks -- 12.8. Historical Background -- 12.9. Appendix: Some Types Of English Determiners -- 13.1. Model Grammar And Some Basic Theorems -- 13.2. Semantic Definition Of Anaphor -- 13.3. 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 -- Greek Alphabet. Edward L. Keenan & Lawrence S. Moss. Includes Bibliographical References And Indexes.