In this section we illustrate context change by showing how our formalism can be used to represent the context of a conversation in which terms have particular meanings that they wouldn't have in the language in general. The analysis that follows is along the lines of .
We examine question/answer conversations which are simply sequence of questions and answers. In this simple model we allow two types of questions:
In order to know what is being communicated in a discourse, as well as reason about a discourse in general, we need a way of representing the discourse. To do this in the framework of the formal theory of context, we identify a new class of contexts, the discourse contexts. Discourse contexts are not only characterized by the sentences which are true in them but also by the intended meaning of their predicates, which might vary from one discourse context to the next.
We represent a discourse with a sequence of discourse contexts, each of which in turn represents the discourse state after an utterance in the discourse. Our attention is focused only on discourses which are sequences of questions and replies: . Thus, we can represent such a discourse with a sequence of discourse contexts:
s.t. (i) is some discourse context in which the initial question ( ) was asked; (ii) the function takes a question and some discourse context (representing the discourse state before the question ) and returns the discourse context representing the discourse state after asking the question in ; (iii) the function takes a reply and some discourse context (representing the discourse state before before replying ) and returns the discourse context representing the discourse state after replying in . In order to reason about the discourse we now only need the properties of the functions and . These will be made precise in the next subsection. Similar representation of discourse in logic is often used by linguists; eg. [54, 7].
Since we are not concerned with solving the syntactic and semantic problems addressed by the natural language community, we are assuming the system is given the discourse utterances in the form of logical formulas. This assumption is in line with ; in McCarthy's terminology we would say that the discourse has been processed by both the parser and the understander to produce a logical theory. Note that the process of producing this theory is not precisely defined, and it is not completely clear how much common sense information is needed to generate it. It might turn out that producing such a theory requires the solution of the problem we had set out to solve. But for the time being let us take a positive perspective and assume the discourse theory is given; for further discussion of this point see [31, 33, 56, 11]. Note that our simple model does not claim to capture all aspects of discourse interpretation. We have refrained from modeling some phenomena that have been studied by semanticists and computational linguists. In particular, Discourse Representation Theory, , includes a third aspect of discourse interpretation, namely discourse entities known as reference markers. Reference markers, each of which can be accessible at a given point in a discourse, are now viewed as an essential element of most theories of context that deal with anaphoric reference. Furthermore, we have ignored pragmatic aspects relevant to discourse analysis; see . These include resolving references by keeping track of which objects are salient in a discourse, and inferring the intentions of agents based on their speech acts.