Semantic underspecification is an essential and pervasive property of natural language. This monograph provides a comprehensive survey of the various phenomena in the field of ambiguity and vagueness. The book discusses the major theories of semantic indefiniteness, which have been proposed in linguistics, philosophy and computer science. It argues for a view of indefiniteness as the potential for further contextual specification, and proposes a unified logical treatment of indefiniteness on this basis. The inherent inconsistency of natural language induced by irreducible imprecision is investigated, and treated in terms of a dynamic extension of the proposed logic. The book is an extended edition of a German monograph and is addressed to advanced students and researchers in theoretical and computational linguistics, logic, philosophy of language, and NL- oriented AI. Although it makes extensive use of logical formalisms, it requires only some basic familiarity with standard predicate logic concepts since all technical terms are carefully explained.