SpeechWeb consists of a collection of hyperlinked natural-language interfaces to applications which can be accessed through the Internet from speech browsers running on PCs. The applications contain hyperlinks which the browser uses to navigate SpeechWeb. The natural-language interfaces have been constructed as executable specifications of attribute grammars using a domain-specific programming language built for this purpose. The approach to natural-language processing is based on a new efficient compositional semantics that accommodates arbitrarily-nested quantification and negation. The user-independent speech browser is grammar based, and novel techniques have been developed to improve recognition accuracy.