A Study of Logics [Hardcover]

It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to name but a few - which have originated in the areas of mathematical logic and computer science. In this book the author presents a systematic study of this rich harvest of logics via Tarski's well-known axiomatization of the notion of logical consequence. New and sometimes unorthodox treatments are given of the underlying principles and construction of many-valued logics, the logic of inexactness, effective logics, and modal logics. Throughout, numerous historical and philosophical remarks illuminate both the development of the subject and show the motivating influences behind its development. Those with a modest acquaintance of modern formal logic will find this to be a readable and not too technical account which will demonstrate the current diversity and profusion of logics. In particular, undergraduate and postgraduate students in mathematics, philosophy, computer science, and artificial intelligence will enjoy this introductory survey of the field.

1. The Multiplicity of Logics
2. Classical Logic
3. Abstract Logics
4. Logical Operations
5. Order and Lattices
6. Constructing Logics
7. Quasi-Boolean Algebras and Empirical Continuity
8. Three-valued Logic
9. Relevance
10. The Calculus of Logics: Effective Logic
11. Modal Logics

Peculiar to this logic text is the author's profound interest in the historical and philosophical foundations of logic (manifest throughout the volume, almost on each page), and even in the sociological connections of this discipline. --Mathematical Reviews