A book on SDRT:

Logics of Conversation

A Brief Summary

In collaboration with Nicholas Asher, we've developed a dynamic semantic theory of discourse interpretation that's called Segmented Discourse Representation Theory (SDRT).

SDRT explores the interplay between discourse interpretation and discourse coherence. It consists of several connected components. First, it supplies a language for representing the logical form of discourse and of dialogue. A discourse is represented as a set of labels, each one standing for a segment of the discourse, and each label is associated with a representation of its content. That content can feature rhetorical relations like Explanation and Contrast between labels. Consequently, a coherent discourse is a segment consisting of rhetorically connected subsegments.

The language is assigned a dynamic semantic interpretation. The interpretations of rhetorical relations often specify additional content to that given by the compositional or lexical semantics of the utterances they connect together. In this way, meaning representations for discourse in SDRT capture those implicatures that arise via assumptions that the discourse is coherent (in other words, that every segment of the discourse is connected to another segment).

SDRT also supplies a so-called glue logic in which one computes the logical form of a discourse, using compositional semantics and non-linguistic information such as real world knowledge as clues. This logic supports default reasoning, since one never has complete and accurate information about the context, including speaker intentions. The axioms of the logic are designed to help the interpreter solve three logically co-dependent tasks in interpretation:

Which part of the old information is the new information rhetorically connected to?
Note that unlike the assumptions underlying Rhetorical Structure Theory, this may be content that was introduced by a non-adjacent segment of the text.

Which rhetorical relation(s) represent this connection?
And

How does this rhetorical connection affect the content of the segments being so connected?
In particular, does it augment any of the partial information about content that was generated by the grammar or resolve any other kinds of linguistic ambiguity?

Taken together, SDRT's glue logic and its dynamic semantics for the logical form of discourse supply a theory for computing pragmatically preferred interpretations of discourse.

Unlike prior theories of discourse interpretation within AI, the reasoning architecture is highly modular, in that the glue logic is distinct from the logic in which those logical forms are interpreted. It's also kept separate from the logic of the lexicon, domain knowledge, cognitive states and so on. The glue logic has only restricted access to these information sources in order to maintain computability.

SDRT offers a novel approach to speech acts, where they are treated as anaphoric relations between utterances (anaphoric because the part of the discourse context that the current utterance is related to via the speech act is anaphorically determined). This contrasts with the more usual conception of speech acts as properties of utterances. In fact, each rhetorical relation can be viewed as a type of speech act. The status of rhetorical relations as actions is reflected in their interpretations: unlike other predicates, they transform the input context (a world-function assignment pair) to a different output one. The output context ensures that the semantic information that's necessary for the successful performance of the speech act has been accommodated. In this way, SDRT provides a logical account of how people bridge the gap between literal and intended meaning. In essence it's a formal theory of how the syntax/semantics interface and the semantics/pragmatics interface interact.

Together with my collaborators, I have used SDRT to model a wide range of phenomena where both semantics and pragmatics interact in complex ways, in particular: nominal anaphora, temporal and causal structures in text and dialogue, word sense disambiguation, lexical sense modulations in context, bridging inferences, presuppositions, metonymy, metaphor, questions and responses in dialogue, imperatives, non-sentential fragments, indirect speech acts, agreement and denial, grounding, non-cooperative conversation, and gesture.