This article first introduces the problem that discourse representation the- ory, in its specific sense, sets out to solve. Then the basic ideas of the theory are listed, various extensions of the basic theory are discussed, the relation to partial interpretation of language is sketched, and proof theory for discourse representation structures is presented. The paper ends with a brief account of the use of ‘unresolved’ discourse representation structures for the representation of ambiguities.
2 The Problem of Unbound Anaphora
The most straightforward way to establish links between anaphoric pronouns and their antecedents is to translate the pronouns as variables bound by their antecedents. This approach does not work when the link crosses a sentence boundary, as in example (1).
A man1 met an attractive woman2. He1 smiled at her2. (1)
It should be possible to interpret the first sentence of this discourse as soon as it is uttered, and then later on, while processing the second sentence, establish the links between the pronouns and their intended antecedents.
One possible solution is translating the indefinites by means of existential quantifiers with scopes extending beyond the sentence level, and then allow the variables for the pronouns to be captured by these quantifiers. But this will not do: at some point the scope of a quantifier has to be ‘closed o↵’, but further on another pronoun may occur that has to be linked to the same antecedent.
The bound variable approach to anaphora also fails for cases where a pronoun in the consequent of a conditional sentence is linked to an indefinite noun phrase in the antedent of the conditional, as in example (2).
If a man1 meets an attractive woman2, he1 smiles at her2. (2)
A possible approach here would be to view (2) as a combination of the noun phrases a man and an attractive woman with a structure containing the ap- propriate gaps for antecedents and pronouns, viz. (3). This is the approach of quantifying-in, taken in traditional Montague grammar (see the article MON- TAGUE GRAMMAR).
If PRO1 man meets PRO2, PRO1 smiles at PRO2. (3)
This approach does not work here, however. Quantifying–in the indefinite noun phrases in (3), i.e. in a structure that has the conditional already in…