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

Ludlow and %Zivanović explore the idea of reducing all of logic to two simple rules sensitive to logical polarity, which has profound consequences for our understanding of human inferential capacities and contemporary linguistics. They introduce a formal relation called p-scope, which controls the operations of their Dynamic Deductive System and proves that it is complete and sound. This system unlocks important properties of natural language, such as restrictedness, which is equivalent to conservativity and is key to understanding quantification and discourse anaphora.

Format: Hardback
Length: 448 pages
Publication date: 24 February 2022
Publisher: Oxford University Press

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 %Zivanović 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.

The idea first explored by medieval logicians 800 years ago is revisited in this book, armed with the tools of contemporary linguistics, logic, and computer science. The Holy Grail of medieval logicians was the notion that all of logic could be reduced to two simple rules that are sensitive to logical polarity, such as the presence and absence of negations. Ludlow and %Zivanović pursue this idea and demonstrate its profound consequences for our understanding of human inferential capacities. They also show its implications for 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 called p-scope, a polarity-sensitive relation that controls the operations that can be carried out in their Dynamic Deductive System. With p-scope in play, deductions can be made using sublogical operations like COPY and PRUNE, which are simple syntactic operations on sentences. Ludlow and %Zivanović 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, such as restrictedness, which they demonstrate to be equivalent to the semantic notion of conservativity. Furthermore, they show that restrictedness is a key to understanding quantification and discourse anaphora, as well as many other linguistic phenomena.

Weight: 766g
Dimension: 241 x 160 x 26 (mm)
ISBN-13: 9780199591534