In the sentence 'Every farmer who owns a donkey beats it,' why does standard first-order predicate logic struggle to handle the pronoun 'it'?
AThe sentence is semantically anomalous and cannot be represented formally at all
BThe existential quantifier for 'a donkey' falls inside the restrictor of 'every farmer,' outside the scope needed to bind 'it' in the matrix clause
CFirst-order logic cannot represent sentences with more than one quantifier
DThe pronoun 'it' must refer to 'farmer,' not 'donkey,' since farmers are mentioned first
In first-order logic, 'a donkey' introduces an existential quantifier (∃y) whose scope is limited to the relative clause 'who owns a donkey.' The pronoun 'it' in 'beats it' falls *outside* that scope, so the variable y is not accessible to bind. Attempts to extend the scope of ∃y to cover the whole sentence produce a different, weaker reading. DRT resolves this by building a DRS in which indefinites introduce discourse referents accessible across the entire conditional structure — 'a donkey' in the restrictor introduces a referent y accessible to the matrix clause.
Question 2 Multiple Choice
A speaker says 'My neighbor just got back from her trip.' The listener has no prior information about any trip. In DRT terms, what happens?
AThe discourse fails — the presupposition of a prior trip cannot be resolved and interpretation halts
BThe presupposition is accommodated — a new discourse referent for the trip is added to the DRS
CThe pronoun 'her' fails to find an antecedent and the sentence is uninterpretable
DThe listener discards the sentence as uncooperative under Gricean maxims
DRT distinguishes anaphora resolution (finding an existing referent) from presupposition accommodation (adding a missing referent when required). 'My neighbor got back from her trip' presupposes that a trip occurred. When this isn't established in the current DRS, the interpreter accommodates — inferring that a trip must exist and adding it as a new discourse referent with the conditions that the speaker's neighbor took it. Accommodation is licensed when the presupposition is plausible and consistent with the existing model. The DRS does not crash; it dynamically expands.
Question 3 True / False
In DRT, each sentence is interpreted independently, and pronouns find their antecedents primarily within the sentence that contains them.
TTrue
FFalse
Answer: False
This describes sentence-level semantics, not DRT. DRT's central innovation is that discourse is interpreted by building a single, cumulative Discourse Representation Structure across multiple sentences. A discourse referent introduced in one sentence (e.g., 'A woman entered' — introduces referent x) remains accessible to subsequent sentences ('She was happy' — the pronoun 'she' picks up x). Pronouns can resolve to any discourse referent currently in scope within the DRS, regardless of which sentence introduced it.
Question 4 True / False
In DRT, whether a discourse referent introduced in a subordinate clause (e.g., the antecedent of a conditional) can serve as an antecedent for a subsequent pronoun depends on the accessibility conditions of the DRS.
TTrue
FFalse
Answer: True
DRT defines formal accessibility conditions specifying which discourse referents a pronoun can pick up. Referents in main boxes are accessible to subsequent discourse. But referents introduced inside subordinate DRS boxes (e.g., the consequent of a conditional, or the scope of a negation) are typically *not* accessible outside those boxes. This explains why 'If a farmer owns a donkey, he beats it' allows 'he' to pick up the farmer (both are in the same conditional structure) but 'I don't own a donkey. *It is brown' fails — the referent introduced under negation is inaccessible outside it.
Question 5 Short Answer
How does DRT handle pronoun resolution across sentence boundaries, and what formal object makes this possible?
Think about your answer, then reveal below.
Model answer: DRT tracks all discourse referents — entities introduced by noun phrases and pronouns — in a Discourse Representation Structure (DRS), a box containing referents and conditions that accumulates across the entire discourse. When a pronoun appears, it resolves by searching the accessible portion of the current DRS for a compatible referent. Because the DRS is updated incrementally with each sentence rather than reset, a referent introduced in sentence 1 remains in scope for pronouns in sentences 2, 3, and beyond, provided the accessibility conditions are met.
This contrasts with purely sentence-level semantics, where each sentence starts fresh. The DRS functions as a formal model of the shared mental space that speaker and hearer build together during discourse. Pronouns are not self-contained — they are instructions to find a referent in this ongoing model. The formalism turns what was an informal notion ('discourse context') into a precise, compositional object whose structure can be reasoned about rigorously.