This document discusses the computation of presuppositions and entailments from natural language text. It begins by defining presuppositions and entailments, and explaining how they can be computed using tree transformations on semantic representations. The paper then provides examples of elementary presuppositions and entailments. It describes a system that computes presuppositions and entailments while parsing sentences using an augmented transition network. The system applies tree transformations specified in the lexicon to the semantic representation to derive inferences. The paper concludes that presuppositions and entailments exhibit computational properties not shown by the general class of inferences, such as being tied to the semantic and syntactic structure of language.