Abstract. In this paper the representation theorem for the class of models of dynamic intensional logic is established. It relies on a particular universal construction resulting from a new axiomatization of the class of models considered.
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 (, ). 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) a formal language, called dynamic intensional logic (DIL), including a distinguished non-empty set of discourse markers;
(II) a class of DIL models;
(III) an interpretation of DIL terms with respect to a given DIL model, state and assignment of values to variables.
(I), (II) and (III) represent a dynamic extension of the respective static counterparts of intensional logic IL as formulated by Gallin  (see appendix A). This introductory part is basically aimed at pointing out the additional dynamic components (see ). 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.