11.3.1 Embedding Semantics

Embedding semantics: DRSs are viewed as partial models.

The idea behind the ``embedding semantics'' is that DRSs are viewed as partial models. Now, what does this mean? Basically, it means that a DRS is true with respect to a model (for example one which describes the real world) if it can be embedded in that model. An embedding succeeds if the discourse referents of the DRS can be mapped onto entities of the model's domain in such a way that all the conditions of the DRSs are fulfilled in this model.

Recall from Chapter 1 that we define models as ordered pairs , with a non-empty finite domain of entities, and an interpretation function mapping constants of the DRS language to elements or tuples of elements of . As usual, we have for an -place predicate symbol . Now consider the DRS for:

``A woman walks a dog.''

This DRS is true with respect to a model if we can find an assignment such that , and . This is the key intuition behind the partial match, and this will give us some idea as to how to define the model embedding semantics for DRSs in a formal way. Viewing assignments as partial functions from discourse referents to elements of , we come to the following definition: