Discourse Representation Theory (DRT) tackles temporal reference in language by using discourse referents and temporal variables. It captures events, states, and their relationships through time, helping to analyze how we talk about when things happen.

DRT breaks down sentences into structures that show temporal info and connections. It handles tense, aspect, and temporal anaphora, making sense of complex time-related language. This approach helps unpack tricky temporal phenomena in everyday speech.

Discourse Representation Theory (DRT) and Temporal Reference

Temporal representation in DRT

• DRT employs discourse referents to symbolize events (bounded occurrences like "John ate dinner") and states (ongoing situations like "Mary is happy")
• Encodes temporal information using temporal variables (t, t1, t2) denoting specific time points or intervals and temporal relations (<, >, =) expressing ordering and overlap between variables
• Captures aspectual properties through the relationship between event time (ET) and reference time (RT)
  • Perfective aspect signifies the event is contained within the reference time (ET ⊆ RT)
  • Imperfective aspect signifies the reference time is contained within the event (RT ⊆ ET)

Discourse analysis with DRT

• Represents temporal structure of discourse using a series of discourse representation structures (DRSs), each capturing temporal information and relations introduced by a sentence or clause
• Establishes temporal relations between DRSs by sharing temporal variables and applying temporal constraints
• Represents tense by relating event time (ET) to speech time (ST) or contextually determined reference time (RT)
  • Past tense: ET < ST or ET < RT (event precedes speech or reference time)
  • Present tense: ET = ST or ET = RT (event coincides with speech or reference time)
  • Future tense: ST < ET or RT < ET (speech or reference time precedes event)
• Represents aspect through the relationship between event time (ET) and reference time (RT) as described earlier

Temporal anaphora resolution

• Resolves temporal anaphora (expressions like "then" or "at that time" referring to previously mentioned times or events) by identifying the antecedent and establishing a temporal relation
• Establishes temporal relations between events by sharing temporal variables (indicating events occur simultaneously) and applying temporal constraints (e1 < e2 specifies ordering)
• Uses principles of accessibility (antecedent must be accessible from current or superordinate DRS) and specificity (chooses most specific antecedent if multiple are accessible) to determine appropriate temporal antecedent

Challenges of complex temporal phenomena

• Progressive aspect challenges DRT as it represents ongoing events without specifying completion, requiring additional temporal variables and constraints (representing the event as a non-completed part of a larger event)
• Narrative progression involves temporal ordering of events, often with implied relations not explicitly stated, requiring DRT to infer appropriate relations based on world knowledge and pragmatic principles
• Complex phenomena like habituals (repeated events), iteratives (repeated subevents), and generics (general statements) may require extensions to basic DRT, such as quantification over events/times or incorporation of aspectual operators