In this chapter we are seeking to outline a semantics that would match the syntactic requirements, introduced in Chapter 2. It is argued that we shall concentrate on ostensive procedure of language acquisition with much more attention than it is usually done. Ostensive meanings are indispensable for the semantics of not only a few simple primitive names, but of many compound names and sentences as well. Thus, a short survey into a prototype/stereotype theory of the meaning of names is made, and a longer excursion to the foundations of situation semantics, in the style of Barwise & Perry's . The problems of ostensive meanings of sentences, semantic entailment and ambiguity of nominalization are discussed.