Dag Westerståhl

A comprehensive introduction to logic’s central concepts. This book provides a concise but detailed account of modern logic's three cornerstones: the completeness of first-order logic, Gödel's Incompleteness Theorems, and Turing's analysis of computability. In addition to the central text, an appendix explains the required technical terminology and facts. The main ideas behind the three cornerstones are explained in a simple, easy-to-grasp manner, and it is possible to select among the chapters and sections so that the reader becomes familiar with these ideas, even if some technicalities are skipped or postponed. A wealth of exercises accompany a wide selection of materials, including the histories and philosophical implications of the three main premises, making it useful as a textbook for undergraduate or graduate courses focusing on any of the three main themes. The material is rigorous and detailed but keeps the main ideas in sight, and there are numerous excursions into more advanced material for curious readers to explore.

Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.

Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, and many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role. Quantifiers in Language and Logic is intended for everyone with a scholarly interest in the exact treatment of meaning. It presents a broad view of the semantics and logic of quantifier expressions in natural languages and, to a slightly lesser extent, in logical languages. The authors progress carefully from a fairly elementary level to considerable depth over the course of sixteen chapters; their book will be invaluable to a broad spectrum of readers, from those with a basic knowledge of linguistic semantics and of first-order logic to those with advanced knowledge of semantics, logic, philosophy of language, and knowledge representation in artificial intelligence.