The theme of this book is fuzzy logic in a narrow sense, a promising new chapter of fuzzy logic. The basic ideas of formal logic were formulated by Lotfi Zadeh in 1975. The aim of this logic is to investigate the wonderful human capacity of reasoning with vague notions by attempting to formalize the 'approximate reasoning' we use in everyday life. A peculiarity of this book is to propose a general framework based on three mathematical tools: the theory of fuzzy closure operators, an extension principle for crisp logics and the theory of recursively enumerable fuzzy subsets. This book is unique in that it treats fuzzy logics which are not truth-functional in nature (as an example, the logic of the necessities, probabilistic logics and similarity-based logics). The book is addressed to people interested in artificial intelligence, fuzzy control, formal logic, and philosophy. It can be used in special post-graduate university studies and in advanced courses. The book is completely self-contained.