11.3.2 Embedding Semantics for DRSs (Definition)

Formal definition of embedding semantics for DRSs.

Assignment verifies a DRS with discourse referents U and conditions C () in a model if there is an extension of with the following properties:

1. is defined for and for all discourse referents occurring in basic conditions in ;

2. If is in then ;

3. If is in then

4. If is in then every assignment that verifies and agrees with on all discourse referents that are not in , also verifies .

5. If is in then either there is an extension of that verifies in or there is an extension of that verifies in ;

6. If is in then no extension of that is defined for all elements of , verifies in .

According to the embedding semantics, two DRSs can have the same truth conditions while having different anaphoric potential. Put differently, the embedding semantics only describes the logical meaning of DRSs, not the discourse meaning. For this reason, the embedding semantics is sometimes referred to as a static semantics. Reformulations of the semantics of DRSs, where the interpretation of a DRS is described as a relation between assignment functions, capture the intuitions behind discourse meaning by describing meaning in terms of context change potential. Such approaches are known as dynamic semantics, and we will give a formal definition for dynamically interpreting DRSs.