We consider question-answer dialogues between participants who may disagree with each other. The main problems are: (a) How different speech-acts affect the information in the dialogue; and (b) How to represent what was said in a dialogue, so that we can summarize it even when it involves disagreements (i.e., inconsistencies).
We use a fully-typed many-sorted language L with a possible-worlds semantics. L contains nominals representing ‘short answers’. The speech-acts are uniformly represented in a dialogue language DL by ‘focus structures’, consisting of a mood operator, a topic component and a focus component. Each stage of the dialogue is associated with a set of ‘information functions’ (g-functions), which are partial functions taking a topic component (representing a question raised) to a set of propositions determined by the corresponding focus component (to the set of answers given to it).
Asserting is answering a question and, hence, it causes a new g-function to be defined. Asking is an attempt to cause the hearer to define a new g-function satisfying certain conditions. A question asked requests a true and complete answer. A reaction answers a question if it satisfies some of the conditions of the question. Indirect questions are viewed as indirect answers.
A dialogue representation consists of: commitment sets, each representing the commitments expressed by one participant; sets of ‘questions under discussion’ associated with each stage of the dialogue, and the common ground, containing the g-functions and representing consistently what was said in the dialogue.
Concepts of informativeness are naturally defined within the theory. Whether an utterance is informative depends on which question it answers and how the question was answered previously. These concepts yield that uttering mathematical and logical truths is as informative as uttering a contingency.