Semantics of Paragraphs

We present a computational theory of the paragraph. Within it we formally define coherence, give semantics to the adversative conjunction "but" and to the Gricean maxim of quantity, and present some new methods for anaphora resolution. The theory precisely characterizes the relationship between the content of the paragraph and background knowledge needed for its understanding. This is achieved by introducing a new type of logical theory consisting of an object level, corresponding to the content of the paragraph, a referential level, which is a new logical level encoding background knowledge, and a metalevel containing constraints on models of discourse (e.g. a formal version of Gricean maxims). We propose also specific mechanisms of interaction between these levels, resembling both classical provability and abduction. Paragraphs are then represented by a class of structures called p-models.