This book is a study of the foundations of model-theoretic semantics. Its central thesis is that one does not need to assume a perfect structural fit between languages and their models in order to characterise the basic semantic notions. In particular, truth-value gaps and gluts can be explained away as local phenomena that do not bring logical disaster in their wake. Varzi's detailed and original account is based on a generalisation of supervaluationary techniques and is illustrated with reference to a range of different types of examples, from sentential logic to type theory. Audience: The book is self-contained and will appeal to philosophers, logicians, linguists and computer scientists.