Introduction. The motivation for the present paper has arisen from a talk given by M. Stokhof on Dynamic Montague Grammar. In the early nineties this has become a hot topic dealing with a dynamic interpretation of natural language, yielding among others an adequate interpretation of anaphoric relations between quantificational expressions and pronouns ([5], [6]). However, we have been not exploring the subject as a whole. We have primarily been interested in the logical setting used to accomplish their linguistic task. The logical setting itself consists of:

(I), (II) and (III) represent a dynamic extension of the respective static counterparts of intensional logic IL as formulated by Gallin [4] (see appendix A). This introductory part is basically aimed at pointing out the additional dynamic components (see [5]). Nevertheless, a full definition of the class of IL models will be given since it is also a building stone for our equivalent axiomatization of the class of DIL models in Section 2. It will also be seen that the latter enables a natural universal construction of a DIL model that finally results in the representation theorem for the class of DIL models.