Language, Form, and Logic: In Pursuit of Natural Logic’s Holy Grail Peter Ludlow

Language, Form, and Logic: In Pursuit of Natural Logic’s Holy Grail  Peter Ludlow- Ebook Instant Download/Delivery ISBN(s): 9780199591534,0199591539,9780192677631, 0192677632

Product details:

• ISBN 10: 0192677632
• ISBN 13: 9780192677631
• Author: Peter Ludlow

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.

Table contents:

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

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