It is well known that a discourse is more than an arbitrary sequence of clauses; a discourse exhibits coherence. The process of establishing coherence is a fundamental part of language understanding: Just as hearers attempt to identify syntactic and semantic relationships when presented with a sequence of words in a clause, they attempt to identify coherence relationships when presented with a sequence of clauses in a discourse. Nonetheless, this process rarely plays a role in theories of linguistic phenomena that apply across clauses.

In this talk, we provide a computational theory of coherence relationships and the inference processes underlying their establishment that is rooted in three types of `connection among ideas' first articulated by the philosopher David Hume -- Resemblance, Cause or Effect, and Contiguity. We then present data which have eluded adequate analysis in several areas of linguistic theory -- including verb phrase ellipsis, gapping, extraction from coordinate structures, and pronominal reference -- and show that the data pattern with Hume's three categories. In each case, we show how a simple account of the constraints imposed by the linguistic form in question interact with those imposed by the process of establishing coherence to explain the elusive data.