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

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 %Zivanovic 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.

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

Peter Ludlow received his PhD in Philosophy at Columbia University in 1985, then worked in Honeywell's Intelligent Interface Systems Group, and taught at Stony Brook University, The University of Michigan, The University of Toronto, and Northwestern University. He is currently a Research Associate in the Center for Logic and Epistemology at the University of Campinas, Brazil and is working on topics ranging from the philosophy of language and epistemology to the ethics of hacking and the philosophical foundations of blockchain technology. Sašo %Zivanovic graduated in Mathematics in 2002, and received his PhD in Linguistics from the University of Ljubljana in 2007. He is currently an Assistant Professor at the Faculty of Arts at the University of Ljubljana. His research interests range from semantics to phonology of natural language, and include the architecture and the evolution of the human language faculty.