The two logical notions of intension and extension are examined and applied to examples of Chinese words. Intension and extension are comparable to "sense" and "reference." It is found that they are not only useful in explaining certain problems concerning meaning, but also cogent in building a formal semantic structure parallel to formal syntax as represented by categorical grammar. It is suggested that some problems remain, such as the fact that these notions seem to deal only with declarative sentences. A need is seen for explanations for idiomatic usages that cannot be accounted for in terms of the Fregean principle, as well as for contextual situations turning a normal sentence into a satirical one. However, intensional grammar is seen as an important first step in its provision of a formal semantic structure. (Author/MSE)