Discourse Representation Theory (DRT)

Origin. Hans Kamp, "A theory of truth and semantic representation" (in Groenendijk, Janssen, and Stokhof, eds., Formal Methods in the Study of Language, 1981), introduced discourse referents and DRS boxes to handle cross-sentential anaphora and donkey sentences, which static Montague semantics cannot bind. Irene Heim's dissertation The Semantics of Definite and Indefinite Noun Phrases (UMass, 1982) reached an equivalent system, File Change Semantics, independently. Kamp and Reyle, From Discourse to Logic (Kluwer, 1993), is the standard reference.

Models. A Discourse Representation Structure is a pair ⟨U, Con⟩ of a set of discourse referents and a set of conditions, and a discourse is interpreted by building one incrementally rather than sentence by sentence. Truth is embedding: a DRS is true in a model iff some assignment of the referents in U to individuals verifies every condition in Con, with sub-DRSs verified relative to the extension of that assignment. Anaphora is not resolved by scope but by accessibility, a structural relation on nested boxes, which is what lets an indefinite bind a pronoun across a sentence boundary that no quantifier could reach.

Formalism.

DRS structure: ⟨U, Con⟩. U: universe (discourse referents). Con: conditions (predicates on referents). Box notation.

DRS box notation: ┌─────────┐ │ x, y │ ← referents ├─────────┤ │ man(x) │ ← conditions │ loves(x,y)│ └─────────┘

Construction rules: Indefinite: introduces referent. "A man" → add x, man(x). Pronoun: picks up referent. "He" → use accessible x.

Accessibility: Referent accessible if in same or superordinate DRS. Not if in subordinate. "If a man comes, he sits" → accessible. "It's not the case that a man comes. *He sits" → not accessible.

Negation: ¬DRS: subordinate box. Referents trapped inside. Not accessible from outside. Scope island.

Conditionals: If DRS₁ then DRS₂. DRS₁ referents accessible in DRS₂. Not outside. Donkey sentences handled.

Donkey sentences: "If a farmer owns a donkey, he beats it." ∀x,y[(farmer(x) ∧ donkey(y) ∧ owns(x,y)) → beats(x,y)]. Indefinite with universal force. DRT explains: the indefinite contributes a free referent; the universal force is the duplex condition's, not the indefinite's.

Truth definition: K = ⟨U, Con⟩ is true in M iff ∃f: U → Dom(M) with M ⊨_f γ for every γ ∈ Con. For K₁ ⇒ K₂: every proper embedding of K₁ extends to one of K₂. For ¬K: no proper embedding of K exists. Embedding, not satisfaction of a formula — the box is the interpreted object.

Accessibility, precisely: U of K is accessible in K itself, in any K' subordinate to K, and from K₁ into K₂ across K₁ ⇒ K₂. Not out of ¬K, not out of a disjunct, not out of the consequent.

Relation to first-order logic: The DRS language translates into FOL and back. No gain in expressive power; the gain is in what is accessible when. Satisfiability is therefore undecidable.

Presupposition (van der Sandt 1992): Presuppositions are anaphors with descriptive content. Bind to an accessible antecedent, else accommodate at the highest permitted site. Projection falls out of accessibility.

Symbols.

Metatheory. DRT is expressively equivalent to first-order logic — DRSs translate to formulas and back — so it adds no new truth conditions, and its satisfiability problem is undecidable for the same reason. What it provides is a different bookkeeping of binding, and what it loses is compositionality: the DRS is a representational level built by construction rules on syntax, which is why Kamp's original system was not a compositional semantics in Montague's sense. Two responses closed the gap. Groenendijk and Stokhof, "Dynamic Predicate Logic" (Linguistics and Philosophy, 1991), gave a compositional, representation-free dynamic semantics agreeing with DRT on the fragment by making meanings relations between assignments; Muskens (1996) gave Compositional DRT by encoding DRSs directly in classical type logic with states. Van der Sandt (1992) reduced presupposition projection to anaphora resolution inside DRT, and Asher and Lascarides, Logics of Conversation (2003), extended it to SDRT with rhetorical relations, since box accessibility alone does not track discourse structure.

Applies to. Computational semantics. Anaphora. Discourse processing. NLP.

Limitations. Unselective binding overgenerates. In "Most farmers who own a donkey beat it" the duplex condition quantifies over farmer–donkey pairs, so a single farmer with many donkeys skews the count — the proportion problem, and it is a wrong prediction, not a gap. The same mechanism forces the strong reading of "Every farmer who owns a donkey beats it" and cannot generate the weak one, so the weak–strong ambiguity needs machinery outside the box calculus. Accessibility is simultaneously too strict and unprincipled: referents under negation are inaccessible, yet modal subordination ("A wolf might come in. It would eat you.") and bathroom sentences ("Either there is no bathroom, or it is upstairs") retrieve them anyway. Since the DRS language is only first-order, satisfiability is undecidable, so no implementation can be complete. And the construction rules are triggered by syntactic configurations, which makes the original theory representational rather than compositional.

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