Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions.

Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions.

Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1, Introduction to Logic, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained.

Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar. It also contains a great deal of original work on categorial grammar and its application to natural-language semantics. The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics. Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language. The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material. Topics covered include higher-order logic, applicative categorial grammar, the Lambek calculus, coordination and unbounded dependencies, quantifiers and scope, plurals, pronouns and dependency, modal logic, intensionality, and tense and aspect. The book contains more mathematical development than is usually found in texts on natural language; an appendix includes the basic mathematical concepts used throughout the book.

This book sets out the foundations, methodology, and practice of a formal framework for the description of language. The approach embraces the trends of lexicalism and compositional semantics in computational linguistics, and theoretical linguistics more broadly, by developing categorial grammar into a powerful and extendable logic of signs. Taking Montague Grammar as its point of departure, the book explains how integration of methods from philosophy (logical semantics), computer science (type theory), linguistics (categorial grammar) and meta-mathematics (mathematical logic ) provides a categorial foundation with coverage including intensionality, quantification, featural polymorphism, domains and constraints. For the first time, the book systematises categorial thinking into a unified program which is at once both logically secured, and a practical tool for pure lexical grammar development with type-theoretic semantics. It should be of interest to all those active in computational linguistics and formal grammar and is suitable for use at advanced undergraduate, postgraduate, and research levels.

Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show that these formal languages are rich enought to be used in the precise description of natural languages. Appendices describe some of the concepts discussed in the text.

The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. - Completely revised and updated - includes over 25% new material - Discusses the interface between logic and language - Many of the authors are creators or active developers of the theories