11.3 Discourse representation and centering theory

Discourse Representation Theory

Discourse Representation Theory (DRT) models how meaning builds up across a sequence of sentences. Rather than treating each sentence in isolation, DRT assumes that interpreting any given sentence depends on the context established by everything said before it. This makes it especially useful for resolving anaphora, since pronouns and other referring expressions often point back to entities introduced earlier in the discourse.

Core Concepts

The central data structure in DRT is the Discourse Representation Structure (DRS). A DRS has two components:

• Discourse referents: entities introduced into the discourse, represented by variables like $x$, $y$, $z$. Every time a new entity is mentioned (e.g., "a farmer," "a donkey"), a new referent gets added.
• Conditions: predicate-argument structures and relations that hold between discourse referents. For example, if the discourse says "A farmer owns a donkey," the DRS would contain referents $x$ and $y$ along with conditions like $\text{farmer}(x)$, $\text{donkey}(y)$, and $\text{owns}(x, y)$.

As each new sentence is processed, its referents and conditions get merged into the existing DRS. This is how meaning accumulates. When a pronoun like "he" appears, DRT resolves it by linking it to an accessible discourse referent already in the DRS. Accessibility is determined by the hierarchical structure of the DRS: referents introduced inside the scope of negation or certain quantifiers may not be accessible from outside that scope.

Centering Theory and Anaphora Resolution

How Centering Theory Works

Centering Theory is a model of discourse coherence that tracks the local attentional state, meaning which entities are most salient at any given point. Where DRT builds a global representation of the whole discourse, centering theory zooms in on the relationship between adjacent utterances.

Each utterance has two key components:

• Forward-looking centers (Cf): a ranked list of all the entities evoked by the current utterance, ordered by salience. Grammatical role is a major factor in this ranking: subjects tend to rank highest, followed by objects, then obliques.
• Backward-looking center (Cb): the single most salient entity from the previous utterance that is also realized (mentioned) in the current utterance. The Cb represents what the current utterance is "about" in terms of continuing the discourse.

Based on how the Cb and Cf relate across two consecutive utterances ($U_{n-1}$ and $U_n$), centering theory classifies four transition types:

1. Continue: $Cb(U_n) = Cb(U_{n-1})$, and $Cb(U_n)$ is the highest-ranked entity in $Cf(U_n)$. The discourse keeps focusing on the same entity in the most prominent position.
2. Retain: $Cb(U_n) = Cb(U_{n-1})$, but $Cb(U_n)$ is not the highest-ranked entity in $Cf(U_n)$. The same entity stays as the center, but something else has taken the most prominent slot, signaling a potential shift ahead.
3. Smooth-shift: $Cb(U_n) \neq Cb(U_{n-1})$, but $Cb(U_n)$ is the highest-ranked entity in $Cf(U_n)$. The discourse has shifted focus to a new entity, and that new entity is now prominent.
4. Rough-shift: $Cb(U_n) \neq Cb(U_{n-1})$, and $Cb(U_n)$ is not the highest-ranked entity in $Cf(U_n)$. The focus has shifted, and the new center isn't even the most salient element. This is the least coherent transition.

The theory predicts that discourses with more Continue transitions feel more coherent and are easier to process, while frequent Rough-shifts make a discourse harder to follow.

Discourse Structure in Anaphora Resolution

Both DRT and centering theory offer tools for resolving anaphoric expressions (pronouns, definite descriptions), but they approach the problem differently:

• DRT resolves anaphora by searching for accessible discourse referents within the DRS. Accessibility is constrained by the hierarchical structure of the DRS, which means quantifier scope and negation can block certain referents from being available. For instance, a referent introduced under negation ("A farmer doesn't own a donkey") may not be accessible for a pronoun in the next sentence.
• Centering theory resolves anaphora by preferring the Cb as the antecedent for a pronoun. If the Cb doesn't fit (due to gender, number, or semantic mismatch), the theory considers other entities in the Cf list in order of their salience ranking.

Comparing the Two Approaches

These two frameworks are best understood as complementary. DRT gives you the structural scaffolding for tracking what's accessible across an entire discourse. Centering theory explains why certain referents are preferred over others at any given moment, based on what's locally salient. Together, they provide a fuller picture of how listeners and readers resolve anaphoric expressions in connected language.