Every pregroup grammar is shown to be strongly equivalent to one which uses basic types and left and right adjoints of basic types only. Therefore a semantical interpretation is independent of the order of the associated logic. Lexical entries are read as expressions in a two sorted predicate logic with $\in$ and functional symbols. The parsing of a sentence defines a substitution that combines the expressions associated to the individual words. The resulting variable free formula is the translation of the sentence. It can be computed in time proportional to the parsing structure. Non-logical axioms are associated to certain words (relative pronouns, indefinite article, comparative determiners). Sample sentences are used to derive the characterizing formula of the DRS corresponding to the translation.