13.2 Anaphora resolution in DRT

Discourse Representation Theory and Anaphora Resolution

Discourse Representation Theory (DRT) provides a framework for tracking meaning across sentences. Rather than analyzing sentences in isolation, DRT builds up a running model of the discourse, which makes it especially useful for figuring out what pronouns and other referring expressions point back to. This process is called anaphora resolution.

Anaphora Resolution in DRT

Anaphora occurs when an expression (like a pronoun or definite description) refers back to something already introduced in the discourse. DRT handles this through Discourse Representation Structures (DRSs), which contain two key components:

• Discourse referents: variables that stand for the entities being talked about (people, objects, etc.)
• Conditions: predicates and relations that describe those referents

When a pronoun like he or it appears, DRT resolves it by searching the DRS for an existing discourse referent that matches in features like gender and number. For example, if the DRS already contains a referent $x$ with the condition farmer(x) and male(x), then a later pronoun he can be linked to $x$.

Definite descriptions (phrases like the book or the red car) work differently. DRT looks for a unique referent in the DRS that satisfies the descriptive content. If someone says "the book" and there's exactly one book-referent in the DRS, the link is straightforward. If no matching referent exists, DRT can use accommodation, which introduces a new discourse referent into the DRS to make the description work. This captures the intuition that speakers sometimes refer to things they assume the listener can identify, even without prior explicit mention.

Constructing and Updating a DRS

Building a DRS for a stretch of discourse follows a step-by-step process:

1. Introduce discourse referents for each noun phrase (NP) you encounter. A sentence like A farmer owns a donkey introduces two new referents (one for the farmer, one for the donkey).
2. Add conditions based on the predicates and relations expressed. For the same sentence, you'd add conditions like farmer(x), donkey(y), and owns(x, y).
3. Resolve anaphoric expressions by linking them to appropriate referents already in the DRS. A follow-up sentence like He beats it triggers a search: he links to the farmer referent, it links to the donkey referent, based on feature matching.
4. Update the DRS as new sentences arrive, adding fresh referents and conditions while keeping the existing ones available.

This incremental updating is what gives DRT its power for multi-sentence discourse. The DRS grows as the conversation progresses, maintaining a record of everything that's been introduced.

Accessibility in the DRT Framework

Not every discourse referent in a DRS is available as an antecedent for every anaphoric expression. DRT enforces accessibility constraints that determine which referents a pronoun can "see."

Accessibility is shaped by the hierarchical organization of DRSs. When a conditional or negation creates a sub-DRS (an embedded box), referents introduced inside that sub-DRS are typically not accessible from outside it. For example, in If a farmer owns a donkey, he beats it, the referents for farmer and donkey are introduced in the conditional's sub-DRS. DRT has specific rules for how these become accessible to the consequent clause.

The general principle: a referent is accessible to an anaphoric expression if it was introduced in the same DRS or in a DRS that is hierarchically higher (a superordinate box). Referents buried in subordinate or parallel boxes are not accessible. This structural constraint mirrors real patterns in how we interpret discourse. You naturally expect pronouns to refer to entities that are still "on the table" in the conversation, not ones introduced in hypothetical or negated contexts.

Challenges of Anaphora Resolution

DRT handles many cases of anaphora cleanly, but several challenges remain:

• Ambiguity: When multiple referents match a pronoun's features, DRT alone can't always pick the right one. John told Bill that he was wrong has two possible antecedents for he. Resolving this often requires pragmatic reasoning or world knowledge beyond what the DRS provides.
• Computational complexity: As a discourse grows longer and accumulates more referents, the search space for resolving anaphora expands. This makes building efficient, scalable DRT-based systems a real engineering challenge.
• Cataphora: Sometimes the referring expression comes before its antecedent, as in Before he left, John locked the door. DRT is primarily designed for backward-looking anaphora (where the antecedent comes first), so handling cataphora requires extensions to the standard framework.