Natural languages presuppose a rich semantic ontology: To interpret the sentence Every boy admires Mary, we assume the existence of individuals (i.e. boys, Mary), pro- positions (Every boy admires Mary), properties of individuals (being a boy), relations between individuals (admire), and many other types of objects. Formal models for natural language semantics (esp. Montague 1973) tame this zoo of objects by assum- ing only a small number of primitive objects and constructing all other objects from these primitives via semantic rules like function-space formation. In this way, Monta- gue (1973) reduces the referents of a basic fragment of English to constructions out of three types of primitives: individuals, possible worlds, and truth-values. However, in the last thirty years, attempts at revising and extending Montague's model have introduced a plethora of models that assume greatly varying sets of primitives. As a result, the zoo of primitive objects has been traded for a zoo of models.

          This project seeks to unify the different models for natural language semantics. In particular, it aims to identify the commonalities of these models with respect to their choice of primitives, disclose coding relations between the different primitives, and use these relations to identify possible reductions between the models. These reductions achieve a unification of the different semantic models. They further yield insights into the requirements on minimal models of a given linguistic phenomenon and contribute to a better understanding of the linguistic type system. Apart from some isolated reductions, such an effort has never been undertaken. However, only this effort allows us to transfer the interpretive success of one model to another.