This book explores the idea that all of logic can be reduced to two very simple rules that are sensitive to logical polarity. The authors show that this idea has profound consequences for our understanding of the nature of human inferential capacities, and for some of the key issues in contemporary linguistics.

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 %Zivanovi¿ 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.

• 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


• Bibliography


• Index