The book is divided into eight parts whose topics are chosen to emphasize application areas of logic, in particular those related to soft computing. Each part demonstrates possible application of logical methods to problems in the respective areas. The book presents a broad variety of fields and issues in which logic provides conceptual, technical or methodological tool. In particular, important topics in foundations of soft computing, including fuzzy logic, multiple-valued logic, theories of inconsistency and ambiguity, theory of rough sets, theories of incomplete information are studied. The book may be seen as a resource to which readers can turn for research horizons and ideas on how logical models and methods can be developed and applied. It is a source for anyone who needs broad perspective on a role of applied logic and a better understanding of logical methods and their applications. All the contributions present new and original results.