MATHEMATICS OF LANGUAGE -- Title page -- Copyright page -- Table of contents -- INTRODUCTION -- COMPUTATIONAL COMPLEXITY, MATHEMATICAL LINGUISTICS, AND LINGUISTIC THEORY -- 1. INTRODUCTION -- 2. THE COMPLEXITY OF MODERN LINGUISTIC THEORIES -- 3. NONCOUNTING AND NATURAL GRAMMARS -- 4. TREE STRUCTURE AND NATURAL GRAMMARS -- 5. BEYOND UNIFICATION GRAMMARS. -- REFERENCES -- EXCEPTIONS TO GENERIC GENERALIZATIONS -- 1. Introduction. -- 2. Some incorrect proposals. -- 3. A more promising approach. -- 4. A brief analysis. -- 5. Conclusion. -- FOOTNOTES -- REFERENCES -- APPENDIX -- THE STRUCTURE UNDERLYING A SEMANTIC DOMAIN -- 1. PRELIMINARIES -- 1.1 PURPOSE AND BACKGROUND -- 1.2 LEVELS OF STRUCTURE -- 2. APPROACHES TO WORD MEANING -- 2.1 EMPIRICAL INVESTIGATION OF SEMANTIC DOMAINS -- 2.2 MODELS OF LEXICON STRUCTURE -- 3. THE VR FRAMEWORK -- 3.1 SPACES AND VOLUMES -- 3.2 FEATURES OF VR -- 3.3 CONSTRUCTING VOLUMES FOR VR -- 3.4 MEANING OVERLAP AND PROPERTY INHERITANCE -- 3.5 PROTOTYPES -- 3.6 REPRESENTATION OF THEMATIC ROLES -- 4. CONCLUSION -- ACKNOWLEDGEMENTS -- REFERENCES -- BINARY RULES AND NON-BINARY TREES: BREAKING DOWN THE CONCEPT OF PHRASE STRUCTURE -- 1. PARSING WITH TWO DIFFERENT PARSE TREES -- 1.1. Why binary rules are necessary -- 1.2. Why computed trees are necessary -- 1.3. The Kleene star -- 2. AUGMENTED PHRASE STRUCTURE GRAMMAR AND BINARY RULES -- 2.1. An implementation of APSG -- 2.2. Rules with unordered constituents -- 3. MORE REASONS FOR REVISING PHRASE STRUCTURE -- 3.1. Discontinuous constituents -- 3.2. Indirect objects in English -- 3.3. Serial verb constructions in Dutch -- 4. CONCLUSIONS -- REFERENCES -- AN INTRODUCTION TO TREE ADJOINING GRAMMARS -- 1. INTRODUCTION -- 2. TREE ADJOINING GRAMMAR FORMALISM -- 2.1 TAG'S WITH "LINKS" -- 2.2 TAG'S WITH LOCAL CONSTRAINTS ON ADJOINING -- 2.3 DERIVATION IN A TAG.

3. MULTICOMPONENT ADJOINING -- REFERENCES -- THE NOTION 'RULE OF GRAMMAR' RECONSIDERED -- 0. INTRODUCTION -- 1. ETIOLOGICAL ANALYSIS -- 2. A FORMAL THEORY OF ETIOLOGICAL ANALYSIS. -- 3. ETIOLOGICAL ANALYSIS IN THE STANDARD THEORY. -- 4. FAILURES OFDIAGNOSTICITY IN OTHER FORMS OF T-THEORY. -- 4.1. In Relational Grammar. -- 4.2. In the Revised Extended Standard Theory. -- 4.3. In Generalized Phrase Structure Grammar. -- 4.4. In Lexical-Functional Grammar. -- NOTES -- REFERENCES -- UNBOUNDED DEPENDENCIES AND SUBJAOENCY IN A TREE ADJOINING GRAMMAR -- 1. INTRODUCTION -- 2. A TAG FRAGMENT FOR ENGLISH -- 3. UNBOUNDED DEPENDENCIES AND SUBJACENCY -- 4 ECP EFFECTS IN A TAG -- 5. EXTRACTION FROM NP -- 6. CONCLUSION -- REFERENCES -- A TOPOLOGICAL APPROACH TO STRUCTURAL EQUIVALENCE OF FORMAL LANGUAGES -- ACKNOWLEDGEMENT -- ON THE DESIGN OF FINITE TRANSDUCERS FOR PARSING PHRASE-STRUCTURE LANGUAGES -- 1. INTRODUCTION -- 2. THE TRANSDUCER -- REFERENCES -- GRAPHS AND GRAMMARS -- (1) The Graphs -- (2) Getting Trees -- (3) The Grammars -- (4) Acceptance -- (5) Weak Generative Capacity -- Comments -- Acknowledgments -- REFERENCES -- DISCONTINUITY AND PHRASE STRUCTURE GRAMMAR -- REFERENCES -- SOURCESOF INTRACTABILITY IN GPSG THEORY -- 1 INTRODUCTION -- 2 COMPLEXITY OF GPSG-RECOGNITION -- 2.1 Formal Specification of GPSG -- 2.2 The Classifications of Complexity Theory -- 2.3 Reduction from 3SAT to GPSG-Recognition -- 3 THE EP PARADOX RESOLVED -- 4 RESTRICTING METARULE APPLICATION -- 5 DEFINING THE RECOGNITION PROBLEM -- 6 THE COMPLEXITY OF SUCCINCTNESS -- 7 CONCLUSION -- 8 REFERENCES -- FORMAL PROPERTIES OF HEAD GRAMMARS -- 1. INTRODUCTION -- 2. HEAD GRAMMARS -- 3. ONE LETTER HEAD LANGUAGES -- 4. SOME MULTILETTER HEAD LANGUAGES -- 5. NULL RULES AND CHAIN RULES -- 6. BASIC CLOSURE PROPERTIES -- 7. SUBSTITUTIONS AND HOMOMORPHISMS -- 8. A PUMPING LEMMA -- 9. SET OPERATIONS.

10. AFL'S AND GSM MAPPINGS -- 11. CONCLUSION -- 12. MORE RECENT DEVELOPMENTS -- REFERENCES -- FINDING NATURAL LANGUAGES A HOME IN FORMAL LANGUAGE THEORY -- 1. CALL HOME -- 2. FINDING FORMAL LANGUAGES A HOME IN NATURAL LANGUAGE THEORY -- 3. WHAT DO MODELS TELL US? -- 4. WHAT FORM SHOULD MODELS TAKE? -- 5. REDUPLICATION AND MIRROR IMAGE REVISITED -- 6. CONCLUSIONS -- REFERENCES -- THEORIES OF LANGUAGE LEARNABILITY -- 1. INTRODUCTION -- 2. ASSUMPTIONS AND NOTATION -- 3. THE CONCEPT OF A LEARNING ALGORITHM -- 4. GOLD'S DEFINITION OF LEARNABILITY -- 5. FELDMAN'S ALTERNATIVE TO GOLD'S DEFINITION -- 6. APPROXIMATE LANGUAGE LEARNING -- 7. MEMORY LIMITED LEARNING -- 8. WHY NOT FINITE LANGUAGES? -- 9. CONCLUSION -- 10. ACKNOWLEDGMENT -- REFERENCES -- REMARKS ON LINGUISTIC SEMANTICS -- 1. SETTING THE TOPIC -- 2. REFINING THE TOPIC -- 3. DISCLAIMER -- 4. A PROBLEM OVERDUE FOR PROMOTION? -- 5. PROBLEMS THAT MAY BE MANAGEABLE -- 5.1. TENSE AND ASPECT -- 5.2. LOGIC AND LEXICAL SEMANTICS -- 5.3. FIRST-ORDER OR HIGHER-ORDER LOGIC? -- 6. SOME UNRULY PROBLEMS -- 6.1. PROPOSITIONAL ATTITUDES -- 6.2. VAGUENESS -- 7. CONCLUSION -- NOTES -- REFERENCES -- ON THE PROGRESSION FROM CONTEXT-FREE TO TREE ADJOINING LANGUAGES -- 1. INTRODUCTION -- 2. GENERALIZING CFL's -- 3. FROM CFL's TO TAL's -- 3.1. LINEAR TAG's -- 3.2. A TREE AUTOMATON FOR TAL's -- 3.3. A STRING AUTOMATON FOR TAL's -- 3.4. A GENERATOR FOR TAL's -- 4. A HIERARCHY FROM GENERATORS -- 5. A HIERARCHY FROM AUTOMATA -- 6. A HIERARCHY FROM GRAMMARS -- 7. CONCLUSIONS -- REFERENCES.