A problem with SDRT's formalization

In this article, a previously unnoticed problem of Segmented Discourse Representation Theory ("SDRT") is discussed and a solution to it is provided. SDRT is a successful theory about discourses in the field of computational linguistics. The theory will be discussed on the basis of its standard account by Asher and Lascarides (2003). The problem relates to SDRT's central principle called "Maximise Discourse Coherence" ("MDC"). Coherence, and in particular MDC, is a central notion for such theories because it is required to explain what makes for a good discourse. MDC is defined in terms of an update mechanism. This mechanism is flawed as it presently stands. Roughly, the problem consists in defining updates as the set-theoretic union of simpler updates. The proposed remedies fix the mechanism locally without requiring fundamental changes to SDRT's explanatory architecture.