Intro to Semantics and Pragmatics Unit 13 study guides

Key Concepts

• Discourse Representation Theory (DRT) provides a framework for representing the meaning of a discourse incrementally as it unfolds
• DRT captures the dynamic aspects of meaning construction by updating the representation with each new sentence or utterance
• Introduces the notion of a Discourse Representation Structure (DRS) as a formal representation of the discourse
• DRSs consist of a set of referents (entities) and a set of conditions (predicates and relations) that hold for those referents
• Referents in a DRS can be linked to entities mentioned earlier in the discourse (anaphora resolution)
• DRT accounts for the interpretation of pronouns, definite descriptions, and other anaphoric expressions
• Presuppositions are treated as conditions that must be satisfied in the context for a DRS to be updated
• DRT has been extended to handle temporal aspects of discourse, such as the ordering of events and the interpretation of tense and aspect

Historical Context

• Developed by Hans Kamp in the early 1980s as a response to limitations of classical theories of semantics (Montague Grammar)
• Motivated by the need to capture the dynamic nature of meaning construction in discourse
• Influenced by the work of Irene Heim on file change semantics and the notion of context change potential
• Emerged alongside other dynamic semantic theories, such as Heim's File Change Semantics and Groenendijk and Stokhof's Dynamic Predicate Logic
• Has been extended and refined over the years to handle a wider range of linguistic phenomena (plurality, tense, aspect, presupposition)
• Continues to be an active area of research in formal semantics and computational linguistics

Formal Framework

• DRT uses a first-order language with variables, predicates, and logical connectives to represent the meaning of a discourse
• A DRS consists of two components:
  • A set of discourse referents (variables) representing entities mentioned in the discourse
  • A set of conditions (predicates and relations) that hold for those referents
• The construction of a DRS is an incremental process, with each new sentence or utterance updating the existing DRS
• DRS construction rules specify how to introduce new referents and conditions based on the syntactic structure and semantic content of the input
• Accessibility constraints govern which referents are available for anaphoric reference at a given point in the discourse
• A DRS can be embedded within another DRS to represent subordinate or hypothetical contexts (conditionals, negation, modality)
• The truth conditions of a DRS are defined in terms of embedding functions that map discourse referents to entities in a model

Discourse Representation Structures (DRS)

• A DRS is a formal representation of the meaning of a discourse at a given point in its development
• Consists of two parts: a set of discourse referents and a set of conditions
• Discourse referents are variables that stand for entities mentioned in the discourse
• Conditions are predicates or relations that hold for the discourse referents
• DRSs are typically represented using a box notation, with referents listed at the top and conditions below
• Example DRS for the sentence "A man owns a dog": $$\begin{array}{|c|} \hline x, y \\ \hline man(x) \\ dog(y) \\ own(x, y) \\ \hline \end{array}$$
• DRSs can be nested to represent complex structures such as conditionals and negation
• The accessibility of referents across DRSs is determined by a set of structural constraints
• DRSs provide a basis for representing and reasoning about the truth conditions of a discourse

Anaphora and Presupposition

• DRT provides a natural account of anaphora resolution, i.e., the interpretation of pronouns and other anaphoric expressions
• Anaphoric expressions are treated as variables that must be linked to accessible discourse referents
• Accessibility is determined by the structure of the DRS and a set of binding constraints
• Pronouns are typically represented as free variables that are equated with accessible referents
• Definite descriptions introduce new referents that must be linked to unique entities satisfying the descriptive content
• Presuppositions are treated as conditions that must be satisfied in the context for a DRS to be updated
• Presupposition triggers (definite descriptions, factive verbs, etc.) introduce conditions that must be matched against the existing DRS
• If a presupposition cannot be accommodated, the DRS update is blocked, and the discourse is judged infelicitous
• DRT provides a principled way of representing and resolving anaphoric dependencies and presuppositional constraints in discourse

Temporal Aspects

• DRT has been extended to handle temporal aspects of discourse, such as the ordering of events and the interpretation of tense and aspect
• Temporal DRT introduces a set of temporal referents (time points or intervals) and temporal relations (precedence, inclusion, etc.)
• Verbal predicates are associated with event variables that are located in time relative to other events and temporal referents
• Tense and aspect markers introduce constraints on the temporal ordering of events and their relation to the speech time
• Example: The sentence "John arrived" introduces an event variable $e$ and a condition $arrive(e, john)$, with the past tense constraining $e$ to precede the speech time
• Temporal anaphora can be resolved by linking event variables to accessible temporal referents in the DRS
• Temporal DRT provides a rich framework for representing and reasoning about the temporal structure of discourse

Applications in Natural Language Processing

• DRT has been applied to various tasks in natural language processing (NLP), such as:
  • Coreference resolution: Identifying and linking mentions of the same entity in a text
  • Temporal information extraction: Extracting and normalizing temporal expressions and ordering events
  • Discourse parsing: Segmenting a text into discourse units and identifying rhetorical relations between them
  • Machine translation: Representing the meaning of a source language discourse and generating an equivalent target language discourse
• DRT provides a structured representation of discourse meaning that can be used as input to downstream NLP tasks
• DRS-based features have been shown to improve the performance of coreference resolution and temporal information extraction systems
• DRT has been used to develop discourse-aware language models that capture long-range dependencies and coherence constraints
• The incremental nature of DRT makes it well-suited for processing streaming or real-time data in NLP applications

Limitations and Criticisms

• DRT has been criticized for its lack of compositionality, i.e., the meaning of a complex expression is not always a function of the meanings of its parts
• The treatment of quantification in DRT is non-standard and can lead to issues with scope ambiguity and donkey anaphora
• DRT does not provide a straightforward way of representing and reasoning about modal or counterfactual contexts
• The formal complexity of DRT can make it difficult to implement and reason with in practical NLP systems
• Some linguistic phenomena, such as bridging anaphora and plural reference, are not easily captured within the standard DRT framework
• DRT has been extended and modified to address some of these limitations (e.g., Compositional DRT, Segmented DRT)
• Alternative frameworks, such as Dynamic Predicate Logic and Update Semantics, have been proposed to overcome some of the limitations of DRT
• Despite its limitations, DRT remains an influential and widely-used framework for representing and reasoning about discourse meaning in formal semantics and NLP.