Language, Form, and Logic: In Pursuit of Natural Logic's Holy Grail

Description

This book takes an idea first explored by medieval logicians 800 years ago and revisits it armed with the tools of contemporary linguistics, logic, and computer science. The idea - the Holy Grail of the medieval logicians - was the thought that all of logic could be reduced to two very simple rules that are sensitive to logical polarity (for example, the presence and absence of negations). Ludlow and Živanović pursue this idea and show how it has profound consequences for our understanding of the nature of human inferential capacities. They also show its consequences for some of the deepest issues in contemporary linguistics, including the nature of quantification, puzzles about discourse anaphora and pragmatics, and even insights into the source of aboutness in natural language. The key to their enterprise is a formal relation they call "p-scope" - a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. They show that with p-scope in play, deductions can be carried out using sublogical operations like those they call COPY and PRUNE - operations that are simple syntactic operations on sentences. They prove that the resulting deductive system is complete and sound. The result is a beautiful formal tapestry in which p-scope unlocks important properties of natural language, including the property of "restrictedness," which they prove to be equivalent to the semantic notion of conservativity. More than that, they show that restrictedness is also a key to understanding quantification and discourse anaphora, and many other linguistic phenomena. Dedication Contents Acknowledgments List of Figures and Tables 1. Introduction 2. Natural Logic 3. Previous Accounts of Polarity Logics for Natural Language 4. L*: A First-order Polarity Logic for Generalized Quantification 5. L**: A First-order Polarity Logic with Plural Domains 6. An Introduction to the Dynamic Deductive System 7. Completing the Dynamic Deductive System 8. Representational Minimalism and Comparison with Other Natural Deductive Systems 9. Conservativity, Restrictedness, and Quantification 10. Restrictedness as a Fundamental Property of Natural Language 11. Linguistic Phenomena through the Lens of L** 12. L**, LF, and Logical Form 13. Remaining Conceptual Issues Appendix: The Mathematical Foundations References Name Index Subject Index