13.1 DRT framework and discourse representation structures

Discourse Representation Theory (DRT)

Discourse Representation Theory (DRT) is a dynamic approach to meaning that tracks how interpretation builds up across multiple sentences, not just within a single one. Traditional semantic theories assign truth conditions to isolated sentences, but DRT models what actually happens when you process a stretch of discourse: each new sentence updates a shared mental structure. This makes DRT especially useful for explaining how pronouns find their referents, how presuppositions get resolved, and how temporal relations between events are tracked.

Components of Discourse Representation Theory

DRT models meaning construction incrementally. As each sentence in a discourse is processed, the representation grows. Three core pieces make this work:

• Discourse Representation Structures (DRSs): These are the central data structures. Each DRS contains two parts: a set of discourse referents (the entities being talked about) and a set of conditions (predicates and relations that describe those entities).
• Construction algorithm: A set of rules that incrementally builds and updates DRSs as new sentences arrive. The algorithm handles introducing new referents, adding conditions, and resolving context-dependent elements like anaphora and presuppositions.
• Accessibility: Not every referent in a complex DRS is available for later reference. DRT defines accessibility constraints that determine which referents a pronoun or other anaphoric expression can link back to. This is what separates DRT from simpler approaches where any previously mentioned entity is fair game.

A few guiding principles tie these together:

• Noun phrases (especially indefinites) introduce new discourse referents into the DRS.
• Conditions express what's true of those referents (properties, relations, events).
• The DRS updates dynamically with each new sentence, so interpretation is always relative to the context built so far.

Construction of Discourse Representation Structures

The construction algorithm follows a predictable process. Here's how it works for simple cases:

1. Take the next sentence in the discourse.
2. For each noun phrase, introduce a new discourse referent into the DRS universe (the set of referents at the top of the box).
3. For each predicate or relation in the sentence, add a corresponding condition to the DRS.
4. If the sentence contains a pronoun, resolve it by linking it to an accessible discourse referent already in the DRS.

Example: "A man walks. He whistles."

After processing the first sentence, the DRS looks like this:

The indefinite "a man" introduces a new referent $x$, and two conditions describe it.

After processing the second sentence, the pronoun "he" is resolved to $x$ (the only accessible referent), and a new condition is added:

No new referent is introduced because "he" is anaphoric, not a new entity.

Quantifiers require more structure:

• Universal quantifiers (e.g., "every farmer") create a complex condition with two embedded DRS boxes: one for the restrictor ("is a farmer") and one for the nuclear scope ("owns a donkey"). A referent introduced inside the restrictor box is not accessible from outside the universal's structure.
• Existential quantifiers (e.g., "a farmer") simply introduce a new referent directly into the current DRS, which is why indefinites make their referents widely accessible.

Negation and disjunction also introduce embedded boxes:

• Negation creates a subordinate DRS box whose content is negated. Referents introduced inside a negated box are not accessible from outside it. This correctly predicts that "A farmer doesn't own a donkey. *It is healthy" sounds odd, because the donkey referent is trapped inside the negation.
• Disjunction introduces two alternative DRS boxes (one for each disjunct). Referents in either disjunct are typically inaccessible from subsequent discourse.

Semantic Content in DRSs

DRSs do more than just list referents and predicates. They encode several discourse-level phenomena:

Anaphora resolution is DRT's signature strength. Pronouns are resolved by linking them to discourse referents that are accessible given the structure of the DRS. Accessibility is governed by the embedding relations between boxes: a referent in a superordinate (higher) box is accessible, but a referent buried inside a negation or the consequent of a conditional is not. This structural approach explains why some anaphoric links feel natural and others don't.

Presuppositions in DRT are treated as conditions that need to be satisfied by the existing context. When you encounter "The king of France is bald," the definite description presupposes that there is a king of France. In DRT terms, the presupposed content forms its own small DRS that must be accommodated into (merged with) the main DRS. If the context already contains a suitable referent, the presupposition is satisfied. If not, the hearer may accommodate it by adding the presupposed information to the DRS, though this accommodation has limits.

Temporal relations are modeled by introducing discourse referents for events and time intervals, not just for individuals. Temporal connectives like "before" and "after" add ordering conditions between these time referents. For instance, "John ate breakfast. Then he left" would introduce two event referents with a condition specifying that the eating event temporally precedes the leaving event.

DRT vs. Other Semantic Theories

Understanding where DRT fits relative to other frameworks helps clarify what it's actually doing differently.

|First-Order Logic (FOL)|Montague Semantics|DRT| |---|---|---|---| |Scope|Single sentences|Single sentences (compositionally)|Multi-sentence discourse| | Meaning model | Static truth conditions | Static denotations built compositionally | Dynamic, incrementally updated structures | |Anaphora|No built-in mechanism for cross-sentential anaphora|Limited; struggles with donkey sentences|Core strength; accessibility constraints handle it naturally| | Context | Sentences evaluated independently | Sentences evaluated independently | Each sentence interpreted relative to prior context |

FOL assigns truth conditions to individual sentences but has no mechanism for tracking how meaning accumulates across sentences. The classic problem: in FOL, "A farmer owns a donkey. He beats it" is hard to formalize because the existential quantifier's scope doesn't extend past the first sentence. DRT was designed precisely to solve this.

Montague semantics builds meaning compositionally from the parts of a sentence, and DRT actually borrows many of its compositional insights. The difference is that Montague semantics treats each sentence as a self-contained unit, while DRT treats sentences as instructions for updating a discourse context.

Advantages of DRT:

• Provides a natural account of cross-sentential anaphora and donkey sentences
• Handles presupposition resolution in a principled way
• Models the incremental, context-dependent nature of real discourse

Limitations of DRT:

• The formalism can get complex, especially once you add embedded boxes for quantifiers, negation, and conditionals
• Some phenomena remain challenging, including bridging anaphora (where the link between a pronoun and its antecedent requires world knowledge, e.g., "I walked into the room. The ceiling was cracked") and discourse relations (how sentences are rhetorically connected, which frameworks like SDRT try to address)