Table of Contents .............................................. v
Detailed Outline ............................................. vii
Acknowledgements ............................................. xix
Part One: The New Formal Linguistics
Chapter 01: Rectification of Phrase Structure .................. 3
Chapter 02: Escape from the Old Formal Linguistics ............ 14
Chapter 03: The Central Result of the New Formal Linguistics .. 21
Chapter 04: The Relationship between Phrase Structure and
User-Friendliness ................................. 27
Chapter 05: Elementary Applications of the New Formal
Linguistics ....................................... 37
Chapter 06: Newly Structured Programming ...................... 45
Part Two: Establishment of the Context-Oriented Language for
Mathematics
Chapter 07: Preliminaries ..................................... 55
Chapter 08: Definition of Colm, the Context-Oriented
Language for Mathematics .......................... 63
Chapter 09: Early Tutorial on Context-Oriented Symbolic
Manipulation ...................................... 76
Chapter 10: The Substitution Operators ........................ 83
Chapter 11: Small-Scale Applications: The Qualified
Quantifier ........................................ 93
Part Three: Fundamentals of Context-Oriented Mathematical
Logic
Chapter 12: The Syntactics of Well-Formed Mathematical
Contexts ......................................... 103
Chapter 13: The Semantics of Well-Formed Mathematical
Contexts ......................................... 106
Chapter 14: Ramification by Scale of Expression .............. 120
Chapter 15: The Central Correspondence between Contexts and
Statements ....................................... 131
Chapter 16: The Relations of Strength and Weakness ........... 135
Chapter 17: Middle-Scale Applications: The Quote-and-Prove
Rules ............................................ 141
Part Four: Development of Rules of Inference for the New
System
Chapter 18: Negations, Complements, and the Dual Symmetry .... 155
Chapter 19: The Theorem on Monotonicity ...................... 161
Chapter 20: The Local Calculus Rules ......................... 170
Chapter 21: The Copy-Migration Rules: Logical Deduction at
a Distance ....................................... 187
Chapter 22: The Look-and-Feel of Formal Deduction in the
New System ....................................... 193
Chapter 23: Large-Scale Applications: Well-Structured
Relativity ....................................... 203
Part Five: The Structure of Deduction and Proof in the New
System
Chapter 24: Overview of Context-Oriented Proof Theory ........ 215
Chapter 25: The First Formalization of Context-Oriented
Proof ............................................ 222
Chapter 26: Interpolation Operators, Their Warrants and
Phrase Structure ................................. 224
Chapter 27: The Second Formalization of Context-Oriented
Proof ............................................ 234
Chapter 28: Meta-Proof of Theoretical Soundness and
Sufficiency ...................................... 243
Chapter 29: A Full Example of Context-Oriented Formal Proof
in Action ........................................ 248
Part Six: Epilogue
Chapter 30: Epilogue ......................................... 257
Glossary ..................................................... 259
Bibliography ................................................. 264
Index ........................................................ 266
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