A discourse is a sequence of sentences. Very often, the interpretation of a sentence in a discourse depends on what preceded it. A clear example of this comes from anaphoric pronouns, such as he, she, and it. Given a discourse such as Angus used to have a dog. But he recently disappeared., you will probably interpret he as referring to Angus’s dog. However, in Angus used to have a dog. He took him for walks in New Town., you are more likely to interpret he as referring to Angus himself.
The standard approach to quantification in first-order logic is limited to single sentences. Yet there seem to be examples where the scope of a quantifier can extend over two or more sentences. We saw one earlier, and here’s a second example, together with a translation.
Angus owns a dog. It bit Irene.
∃x.(dog(x) & own(Angus, x) & bite(x, Irene))
That is, the
dog acts like a quantifier which binds the
it in the second sentence. Discourse
Representation Theory (DRT) was developed with the specific goal of
providing a means for handling this and other semantic phenomena which
seem to be characteristic of discourse. A discourse representation structure (DRS)
presents the meaning of discourse in terms of a list of discourse
referents and a list of conditions. The discourse referents are the things under
discussion in the discourse, and they correspond to the individual
variables of first-order logic. The DRS
conditions apply to those ...