The source and target calculi each have their own set of basic types, motivated by syntactic and semantic considerations respectively.  At the syntactic end, one could discriminate between sentences s, noun phrases np, common nouns n, for example.  At the semantic end, for a simple extensional interpretation, one could introduce two basic types, e and t. Set-theoretic interpretation for the semantic types is then given in terms of a non-empty set of individuals/entities E and the truth values {0,1}. Denotation domains Dom(A) for semantic types A are set up such that Dom(e) = E, Dom(t) = {0,1} and Dom(A\B) = Dom(B/A) is the set of functions from Dom(A) to Dom(B).