The answer to the question "How can we understand and use a definition?" provides new constraints on natural language and on the internal language in which meaning is mentally represented. Most syntax takes the sentence as the basic unit for well-formedness, but definitions force us to focus on words and phrases, and hence to focus on compositional syntax in parallel with compositional semantics. This study examines both dictionary definitions and definitions from textbooks, from the point...

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In...

This revised and considerably expanded 2nd edition, published in 2008, brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are exp...

Syntax is the system of rules that we subconsciously follow when we build sentences. Whereas the grammar of English (or other languages) might look like a rather chaotic set of arbitrary patterns, linguistic science has revealed that these patterns can actually be understood as the result of a small number of grammatical principles. This lively introductory textbook is designed for undergraduate students in linguistics, English and modern languages with relatively little background in the ...

Andrew Radford has acquired an unrivalled reputation over the past thirty years for writing syntax textbooks in which difficult concepts are clearly explained without the excessive use of technical jargon. Analysing English Sentences continues in this tradition, offering a well-structured introduction to English syntax and contemporary syntactic theory which is supported throughout with learning aids such as summaries, lists of key hypotheses and principles, extensive references, handy hin...

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of ...

'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incomp...

Understanding Minimalism, first published in 2005, is an introduction to the Minimalist Program - the model of syntactic theory within generative linguistics. Accessibly written, it presents the basic principles and techniques of the minimalist program, looking firstly at analyses within Government and Binding Theory (the Minimalist Program's predecessor), and gradually introducing minimalist alternatives. Minimalist models of grammar are presented in a step-by-step fashion, and the ways i...

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of...

Syntax: Basic Concepts and Applications provides a systematic introduction to core topics in syntax, focusing on how the basic concepts apply in the analysis of sentences. Assuming no background in linguistic analysis, the book gives students a working knowledge of syntactic analysis from a minimalist perspective. Step by step it explains the fundamentals of phrase structure, movement and deletion. Well-placed exercises throughout reinforce and extend the concepts and analyses presented in...

This book presents the author's research on automatic learning procedures for categorial grammars of natural languages. The research program spans a number of intertwined disciplines, including syntax, semantics, learnability theory, logic, and computer science. The theoretical framework employed is an extension of categorial grammar that has come to be called multimodal or type-logical grammar. The first part of the book presents an expository summary of how grammatical sentences of any l...

Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra.Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Sta...