All humans can interpret sentences of their native language quickly and without effort. Working from the perspective of generative grammar, this volume investigates three mental mechanisms that are widely assumed to underlie this ability: compositional semantics, implicature computation and presupposition computation. For all three mechanisms, formal models have been advanced recently that are accurate for many cases. There is some consensus in the field, however, that further progress requires stronger interconnections between these results. This collection brings together experts from semantics and pragmatics who push this agenda forward. From this perspective, the contributors develop new insights into important empirical phenomena; for example, individual level predicates, free choice effects, presupposition accommodation, exhaustivity effects, specificity. With contributions by many leading researchers in the field, this book will be a useful source for both researchers and students interested in sentence interpretation and language use.