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Discourse Representation Theory models discourse by building structured Discourse Representation Structures. Each sentence adds referents and conditions; pronouns resolve to established referents. This handles anaphora and presupposition accommodation in extended discourse: 'A woman entered. She was happy' succeeds, but 'A woman entered. She had three children' accommodates missing information.
Your study of discourse analysis and formal pragmatics gave you two things: an understanding that meaning extends beyond the sentence, and some tools for thinking about how context shapes interpretation. Discourse Representation Theory (DRT), developed by Hans Kamp in the 1980s, provides the formal architecture that makes those intuitions precise. Its central insight is deceptively simple: to understand a discourse, you don't just interpret each sentence in isolation — you build a running mental model, and each new sentence updates that model.
The formal object DRT introduces is the Discourse Representation Structure (DRS), which you can think of as a box containing two things: a list of discourse referents (roughly, the individuals the discourse has introduced) and a list of conditions (propositions that are true of those referents in the model). When you hear "A farmer owns a donkey," the DRS box gets two new referents — call them *x* (the farmer) and *y* (the donkey) — plus the conditions *farmer(x)*, *donkey(y)*, and *owns(x,y)*. Nothing about this is exotic yet. The payoff comes with anaphora. When the next sentence is "He beats it," the pronouns *he* and *it* need to find antecedents. DRT says they can access the discourse referents already in scope: *he* can pick up *x* (the farmer), *it* can pick up *y* (the donkey). The conditions *beats(x,y)* get added to the same box. The discourse is now a single structured representation rather than two independent sentences.
This matters because it solves the donkey anaphora problem — a famous puzzle in formal semantics. "Every farmer who owns a donkey beats it" seems simple, but the pronoun *it* cannot be a simple variable bound by "a donkey" in the scope of "every farmer," because the scoping doesn't work out. DRT handles it elegantly: the indefinite "a donkey" inside the restrictor of "every farmer" introduces a referent that is accessible to the pronoun in the matrix clause, because both are inside the same conditional DRS structure. The box architecture tracks accessibility in a way that standard predicate logic does not.
Presupposition accommodation is the other major application. When someone says "A woman entered. She had three children," the second sentence presupposes the existence of three children — information not previously established. Rather than crashing, the discourse interpreter accommodates the presupposition by adding the three children as new referents to the DRS, inferring that they must exist because the sentence requires them to. DRT provides a principled account of when accommodation is possible (the presupposition is plausible and consistent with the model) and when it fails. This connects directly to the formal pragmatics you studied: accommodation is the mechanism by which context is dynamically enriched as discourse unfolds. The DRS is not a static representation of a situation; it is the record of an ongoing interpretive process in which each sentence both draws on and updates the shared context that speaker and hearer are building together.